"I will have done it" or "I will have it done"?

Both are correct.

The first sentence states that by an undefined time you yourself will have performed a certain task.

The second sentence states that you are undertaking to ensure that the task is performed, even if you don't do it yourself.

I think putting it into context makes the difference:

Person A: "I need [something] done by lunchtime."

Person B: "I will have it done by then."

Implies that Person B had not necessarily planned to complete the task by lunchtime, but now will because Person A has explicitly asked.

Person A: "I need [something] done by lunchtime."

Person B: "I will have done it by then."

Implies Person B would have completed the task by lunchtime regardless of Person A's statement.

Both are correct but, depending on the situation, one may not be appropriate.

The former response from Person B is submissive; Person A could be an employer giving an instruction to an employee, who confirms that the instruction will be carried out. The latter response could be seen as dismissive; Person B is stating that the instruction is redundant. Some employers may regard the latter as flippant, as if Person B feels he/she doesn't need to be given instructions.

Alternatively, the order of the words could be used to stress the importance of 'it' being 'done':

Person A: "I will help you do it tonight."

Person B: "I will have done it by then!"

If you change the response to 'have it done' it feels less powerful.

The first sentence ( I WILL HAVE DONE IT) is Future perfect. as you mentioned the structure is SUBJECT + WILL + HAVE + PAST PARTICIPLE.

but the second is simple future of passive causative.

if you read about causative, you will see that we have some verbs like (MAKE, GET,HAVE) that we can use in both active and passive forms to talk about an action when the action itself is the point of our sentence not necessarily the doer.

let me help you with giving an example of SIMPLE PRESENT TO CAUSATIVE first, then we change it to FUTURE so you may be less confused.

ACTIVE: I have my mother do my homework.

PASSIVE: I have my homework done ( by my mother) --> in this form the doer is not important. it can even be you.

now if I shift the tense of these two sentences to FUTURE they will be:

ACTIVE: I will have my mother do my homework.

PASSIVE: I will have my homework done (by my mother)

I wish you find it useful. :)