"I will do it by Friday" is the most common and the verb is in the simple future. "I will have it done by Friday" is less common and possibly ambiguous. It could be the "causative have" in the future perfect and mean "I will have somebody do it by Friday," or it could simply be in the future perfect and mean "By Friday, I will have already done it." "I will have done it" is in future perfect and means "By Friday, I will have already done it." Here is a Google N-gram for "we will do it," "we will have it done," and "we will have done it." https://books.google.com/ngrams/graph?content=we+will+do+it%2Cwe+will+have+done+it%2Cwe+will+have+it+done&year_start=1800&year_end=2000&corpus=16&smoothing=3&share=&direct_url=t1%3B%2Cwe%20will%20do%20it%3B%2Cc0%3B.t1%3B%2Cwe%20will%20have%20it%20done%3B%2Cc0

Hi Katya! Other native speakers might have different opinions (it might be a question of where you're from!) but to me they both mean more or lesson the same thing. I'd say they're both correct in spoken English (although I would always say 'I'll' instead of 'I will') but 'I'll have it done by Friday' puts more emphasis on the completion of the action. I feel that the first option sounds a bit more relaxed, whereas the second one carries a bit more weight; it might be in relation to a deadline or something, and you're confidently telling your boss that it'll definitely be done by Friday! Hope that helps :)

The other possibility is "I'll have it done by Friday". That's a natural alternative to "I'll do it by Friday", focusing on the result rather than on my actions. "I'll have done it by Friday." isn't wrong but wouldn't be natural unless there is specific context where you are talking about your actions with respect to future events.

"I'll do it by Friday" sounds more everyday in the spoken language. "I'll have done it by Friday" sounds more standard in the spoken language.