Some gentle clarification: by the time Australia and Japan went to war against each other, the latter had already suffered a number of relatively minor but symbolically significant defeats in China (contemporary observers saw these as challenges to the myth of Japanese invincibility), most notably at Taierzhuang and Changsha.

Mark Johnston's Fighting the Enemy: Australian Soldiers and their Adversaries in World War II (Cambridge: Cambridge University Press, 2000) deals directly with your question and seems to confirm that the Germans held the Australians in high regard. To quote some passages from the chapter "The Germans: Mutual Respect":

An Australian in another battalion reported that German prisoner he met in July 1942 claimed that the Australians had gone home, but that English troopers were continuing to 'dress up as Australians to frighten us'. (52f.)

Early in the siege [of Tobruk], the German commander, Rommel, described Australians as 'fighting magnificently' and showing 'remarkable tenacity'. In a well-known passage he described a group of fifty or sixty Australian prisoners as 'immensely big and powerful men, who without question represented an élite formation of the British Empire, a fact that was also evident in battle'. (53)

A German infantry major described the Australians at Tobruk as 'extraordinarily tough fighters', superior to the Germans in their use of camouflage and individual weapons, particularly as snipers. German accounts of the desert campaigns describe the Australians at Tobruk as 'crack shots', delivering 'incredibly accurate' fire. A mortally wounded German infantryman ... said, as he smoked a cigarette, 'Thank you, you very good fighters'. Another German captured at Tobruk in vicious hand-to-hand fighting during the first German attacks on the 2/17th Battalion, told one of his wounded captors, 'Australian soldiers are very brave', to which an Australian in the party replied 'My bloody oath'. (54)

Early in October 1942, a German intelligence summary concluded that the Australians were, in attack, the best British troops on the Alamein front. At about the same time, General Stumme, the acting commander of the German-Italian Panzerarmee, told a conference of commanders that Australians were the enemy's 'best troops'. Similarly, in 1983 a German writer claimed that the General Staff of Panzerarmee Afrika had considered Australian soldiers 'the best we found in Africa'. (56)

The Japanese, on the other hand, appear to have had much more ambivalent views on the Australians, and Johnston notes that this likely began with Japanese propaganda, which emphasized the inferiority of non-Japanese. Concerning the Australians' military performance, I again quote from Johnston:

... a Japanese wartime account of fighting at Ayer Bemban, in Malaya, said that despite continued Japanese attacks, 'the [Australian] warriors continued suicidal resistance like wounded boars'. It described an Australian counterattack, which won them a brief respite before retreating: 'the enemy, defying death, strangely and impudently counter-attacked with bayonets along the whole line'. Similarly, a propagandistic Japanese article about the Japanese capture of Ambon said that the 'desperate resistance of the Australians after the breakthrough was not to be despised'. (124)

The instructions [to Japanese forces in Papua in 1942] depended on information based on clashes which had occurred earlier at Rabaul and Kokoda, and included the assertion that 'The fighting spirit of the Australian infantry soldier is strong'. This spirit was said to be superior to that of the American troops in the area. The instructions highlighted Australian marksmanship, and the skilful Australian use of cover and grenades. On 11 August, a Japanese lieutenant on the Kokoda Track conceded: 'Although the Australians are our enemies, their bravery must be admired'. (125)

A Japanese intelligence summary written in November, possibly in reference to the Milne Bay operations, said that the Australian soldier's 'will to resist is strong and though we attack him, he resists further'. It also told of Australian skill in the use of hand grenades, and a diary written at about the same time at Gona said 'Their firing is very accurate'. A Japanese diary entry, written at this desperate point, admitted: '27th November- Strength of Australian soldier is superior to that of Nippon soldier'. (125)

... a comment appeared twice in a Japanese report on fighting on the Huon Peninsula that 'Sniping at the enemy is easy and gives substantial results'. In an echo of the Australian assertions that Japanese did not like 'cold steel', Japanese soldiers were told after the Milne Bay battle: 'Enemy lacks fighting spirit in hand to hand combat'. A pamphlet captured the following year said that 'The enemy cannot stand up to hand-to-hand fighting or charges'. Not only could they not face charges, according to the official line, they also could not make them... These criticisms of Australian courage were directed towards the conclusion that the Australians, with their 'materialistic civilisation', were spiritually weaker than the Japanese. (125f.)

In addition, Japanese reports and recollections frequently emphasized the superior firepower available to the Australians and Americans, which the Japanese would need to overcome through their "spiritual superiority." This complements the views of one veteran, Ogawa Masatsugu, who "drew a contrast between conditions in China, where the dead fell in man-to-man conflict with a 'real enemy', and New Guinea, where 'we didn't know what was killing us'." (127) He seems to have had a low opinion of the Australians overall. To quote Johnston again:

Masatsugu was rather scathing about Australian infantry, saying of the early success in the counterattack of October 1943: 'I was amazed how weak the Australian soldiers seemed'. Australians supposedly ran when attacked, and returned to mop up only after artillery, aircraft and exhaustion had robbed the Japanese of their ability to resist. (127)

As an odd footnote to all this, after the war the famous Japanese officer Masanobu Tsuji offered his personal assessment ("the subjective view of just myself") of the fighting prowess of the enemy soldiers that he faced. The Australians here ranked fifth in a list of twelve, at least under hypothetical measures (Masanobu Tsuji's 'Underground Escape': From Siam after the Japanese Surrender, ed. Nigel Brailey [Leiden: Brill, 2012], 235):

If we were to assume that we could give the same equipment and the same training and assume that a fight is waged on the same battlefield, on the basis of actual combat experience in eight years of front-line fighting, I would place the fighting strength of the soldiers of various nations that I fought against in the following order (Japanese soldiers excepted):

1. Chinese

2. Soviet

3. Indian-Gurkhas

4. American

5. Australians

6. Other India

7. English

8. Filipino

9. Burmese

10. Thai

11. Annamese

12. French

I highly recommend Johnston's work if you want a fuller picture of the complexities of this subject. I simply repeated the material that related directly to your question. :)

EDIT: I forgot to include the Italians, whom Johnston does briefly discuss. It seems, in general, that the Italians feared the Australians, due in part to misinformation (apparently spread by Italian commanders) that the Australians behaved like "barbarians" and "took no prisoners." (22f.) At Alamein, the Italians also attributed the Australians' successes to inebriation. Per one Italian division commander: "The enemy generally attacks with very well-trained troops ... These special units, generally Australians and New Zealanders, attack with decision and brutality generally rendered bestial and brutal by drunkeness." And according to another officer: "Hand-to-hand fighting is going on. The Australians, roaring drunk on whisky, are like madmen ... The wounded, both German and Italian, have horrifying tales to tell." (23). Johnston dismisses these claims as explanations or excuses for impending Italian defeats.