A: I have a pet jaguar. (Note: you can insert any animal here instead of a pet jaguar, you can also think of a more reasonable sentence, like "There's a new jaguar in our local zoo.")

B: What sex is it?

A: It's

What is person A going to say? It's HE/SHE? Just HE/SHE? (It's) male / female? Something else?

What if it is an animal that does have separate terms for the two sexes? (tiger, dog...).

Thank you in advance.
As long as you don't say "She's male" or "He's female" you can probably mix and match: It's female, she's female, it's a "she," she's a "she," etc.
It's a "she/ he".Emotion: big smile

Male or female would also work fine.
 BarbaraPA's reply was promoted to an answer.