They didn't bring any camels when they invaded the Iberian Peninsula, or at least the sources on the Muslim invasion such as the Chronicle of 741 or the Chronicle of 754 do not mention the presence of any camels, and it would not be out of ignorance of the existence of such an animal, as the beast was well known in Visigothic Spain.

What's even weirder is the provenance of the camels, besides the Exarchate of Africa: France. Every time camels are mentioned in the sources, they are related to something Frankish or straight up coming from France. What are camels doing in France? Well, we are talking of the early Middle Ages, 6th and 7th centuries, when the Eastern Roman Empire was the mirror upon which any self-respecting sovereign would model himself, and this included not only fashion, but also ceremonies and all sorts of peculiarities, which included the presece of odd beasts such as camels.

The camels in Spain, though, did not get that much consideration. The most prominent presence of camels in the Visigothic period is related to the ceremony of "decalvatio", the ritual of shaving a person's head and beard, thus making him inelligible for the crown. The most famous example of the decalvatio comes from the time of king Wamba, who faced a rebellion led by Paul, Duke of Septimania (modern day Pyrénées Orientales and a bit more). Wamba managed to quell the revolt, captured the duke Paul and brought him as prisoner to the capital city of Toledo. There he paraded Paul on a camel, though another source mentions a wagon moved by camels, and on the most important square had him publicly decalvated. The use of the camel for this ceremony is purely caricaturesque in nature, as for the visigoths and many others the camel looked like a grotesque caricature of what a noble horse would look like, so it was logical that a failed rebel would be subject to public ridicule. Camels were also considered inadequate for military uses, being completely inferior to horses. They were somewhat useful as load carrying animals, and there are some mentions of camels used in Toledo to carry loads of water up the city.

You mention that the most of the South of Spain is very desert-like, when that is extremely far from the truth. The South of Spain was, and still is, extremely fertile, though the climate is hotter than in the north. The valley of the Guadalquivir has some phenomenally fertile sides, and some of its tributary rivers are also fertile. But even if it was desert-like, the camels would have still been of hardly any use given that the main characteristic is not a desert but mountains, for which horses are more suitable. In the South of Spain you have the Penibaetic and Subbaetic mountain systems south of the Guadalquivir, and Sierra Morena to the north.

The Muslim troops by that moment did not have camels by then, they used horses. You could find camels in the armies of Northern African kingdoms or polities such as the kingdom of the Dorsale, Altava, or the Auresian confederation. During the Umayyad conquest of North Africa there is precisely one case when we see camels being mentioned, but they are not on the Muslim side, but on the Auresian. In the battle of Wad-Nini (or Oued-Nini) also known as "the battle of the camels", Kahina used her army's load-carrying camels as a means of hiding a large number of troops he used to surprise and defeat Hassan ibn Numan.