I want to eat, but if I do, I'll get fat.
My attempt at a translation:食べたいけどそれをすると太る.
I expect this is totally unnatural. Even if it is okay I fear that adding それを may make it sound quite formal, but leaving it out just seems totally weird.
Is there a natural way to express this "if I do" part that doesn't repeat the previous verb? If not, is it natural in Japanese to just repeat the verb? This would be a bit clumsy in English.
As you suspected, it's best to repeat the verb.
食べたいけど食べると太る。
Unlike English that requires you to say "I" twice, Japanese allows you to omit everything other than the verb itself. IMO the Japanese way is not that inefficient.
That said, saying それをすると is not bad, either. It sounds a bit stiff, but it's not unnatural as long as it's said by a mature adult. Note that you cannot drop それを when the substituted verb is a godan/ichidan verb. You can drop それを when the original verb is a suru-verb.
Technically, this "do" is a pro-verb (代動詞). Related: “But when I do..”
Using それをすると is not incorrect, just weird. However, what する doing here is not substituting the verb, but doing the same as in「家事をする」or「掃除をする」- performing the action that is interpreted as a noun (Sorry there might be a better way to explain in English; I'm doing my best)
The actual substitution happens at それ, which works as a noun "the action of eating", we just usually shorten it since it's apparent what we're meaning.
To conclude,
食べたいけどそれをすると太る - the full sentence
食べたいけどすると太る - omitting the noun
食べたいけど太る - even this is okay
