It is not true: at the latest by 1961, education alone was not a qualification. There were a lot more voter-suppression techniques than that.

There's a nice general overview of Rhodesian electoral processes and results from the rise of the Rhodesian Front to the end of Rhodesia in Lemon, Anthony. "Electoral Machinery and Voting Patterns in Rhodesia, 1962-1977." African Affairs, vol. 77, no. 309, 1978, pp. 511–530. JSTOR, JSTOR, www.jstor.org/stable/721963.

He has Table 1, a helpful chart for qualifications for voting in 1961 and 1976. He does not list specific changes in between (the 1969 Constitution, most notably), but there's not a major philosophical change between the dates. With a negligable number of exceptions, qualifications always involved money (income would always qualify; in all but one case in 1961, property value could substitute for income). Sometimes age was a factor. Education would reduce, but would not eliminate, the money qualification. For example, in the 1961 B roll, qualification c (#2) is "For persons over 30 years of age, income #120 (6 months) OR property #250 PLUS primary education (completed)"; in 1976, qualification a was "Income $780 (2 years) OR property $1,560".

There were lots of other voter suppression parts, aimed mostly at Africans but also sweeping up poorer Europeans, as in the US South.

The voter had to be a Rhodesian citizen, and a lot of immigrants didn't bother to take out citizenship.

For the lower house, there were two voter rolls, A and B. A had much higher qualifications than B. In 1962, the vast majority of A voters were Europeans. A voters elected many more seats. In 1962, 50 A versus 15 B, and the A voters could influence B elections and vice versa. From 1969, 50 A versus 8 B ... and the A roll was explicitly limited to Europeans (interestingly, including Asians and Coloureds!) and B roll for Africans; 8 more seats elected by a electoral colleges of a small number of African chiefs, headmen, and such.

The European electorate was less than 100,000 out of roughly 200,000. "Estimates of the numbers of Africans actually qualified to vote vary, but 50,000 is perhaps not an unrealistic figure.", out of a total that passed 4,000,000; "[t]he Rhodesian electorate represents less than 0.3% of Africans of voting age".

In 1962, there were no racial qualifications, so in theory, if all Africans had gotten rich, or if the money requirements had been reduced, they could have taken over. From 1969, the number of African (B) seats could increase as the share of income tax paid by Africans increased, but would never exceed the number of A seats. ("This formula also ignores the relatively larger share of indirect taxation, especially sales tax, paid by Africans.").

In 1962, the legislature was unicameral, the House of Assembly. In the 1969 Constitution, a Senate was introduced, but 10 were elected by the lower house, 10 by electors of African chiefs, headmen, and such, and 3 appointed by the President. The Rhodesian Front had all European 50 lower-house seats from the 1965 election [*], so they controlled the Senate and could almost single-handedly muster the 2/3 required for amending the 1969 constitution (they had 57%).

[*] They didn't gerrymander or do anything else to skew the vote to themselves. They didn't have to. For one thing, the opposition was often unorganized. Also, as the Rhodesia Herald noted on 13 April 1970,

Friday's voting is indicative of European willingness to sacrifice the two-or-more party system in order to safeguard white political control. Henceforth no matter how unsatisfactory the Government record may be when it has to go to the country, support for any rival European party is likely to be nervously and hesitantly given for fear of dividing white representation and giving black representation greater leverage.

The reason why "the numbers of Africans actually qualified to vote vary" is because Africans started boycotting elections in 1962, and did so more and more in later elections; in the 8 popularly elected B seats in 1977, "five were returned unopposed, and in the other three seats the poll was only 20.2%."