OP, keep your time off to yourself.
I think it would be a huge ask and I don't think you are under any obligation whatsoever to offer or say yes if asked.
I have various nephews and nieces and I never ever once, even for a second felt the slightest inclination to give up a week of my time to spend time with them.
Nor have I ever heard a friend feel so inclined.
It would never occur to me.
Pre children I looked after the baby of a very close friend a couple of times so she could have a long leisurely lunch as all grandparents were past, but we were very close friends and the baby was about 12 months.
3 months is a very small baby and I cannot imagine wanting to leave him with anyone but his father.
Not your responsibility in any shape or form.
Enjoy your leave.
@ScattieHattie1 I think making a decision to return to work after 8 weeks with proper childcare in place due to necessity is a bit different to trying to impose on a person who might be on their annual leave to look after your newborn.
I would feel huge compassion for any woman who felt the need to return to work after 8 weeks for medical reasons.