In both languages the subject is the whole part that is before (the optional) comma.
Die Wüste auf dem Rücken eines Kamels zu durchqueren
To cross the desert on a camel's back
The subject is not only the first word. So the noun phrase "Die Wüste" and the verb "to cross" do not function as a subject alone. Actually, a verb can never function as the subject, unless it is part of a longer phrase as given in this example.
When a infinitive phrase is the subject, the comma is optional. The only purpose of the comma is merely clarification.
The comma is obligatory if you use the pronouns es or das as subject:
Es war einfach berauschend, die Wüste auf dem Rücken eines Kamels zu durchqueren.
Die Wüste auf dem Rücken eines Kamels zu durchqueren, das war einfach berauschend.
The rule that applies is §75.
With respect to the word order, you do not apply the word order of your source to the target language. Instead you put the words in the order which is most natural in your target language. German and English do not follow the exact same word order although the standard word order (S-P-O) is indeed identical.
In German I can see only one possible other word order (swapping "Die Wüste" and "auf dem Rücken eines Kamels") but the given one is the most natural one. Not sure about English, but I guess this is the only possible variation.
On a side note:
The comma would be wrong if the sentence were:
Das Durchqueren der Wüste war einfach berauschend.