You don't sound very family based, you have a DC from previous relationship but he has nothing to do with her, she's just your responsibility?
On my maternity leave I looked after my DS but also did housework, washing and cooking and cleaning.
A baby doesn't generally require constant attention through the day that it stops you sticking a load of washing on, or picking up something on the stairs on your way up.
I wouldn't expect DH to come home after work then cook me dinner because I've been looking after a baby, I'd get dinner ready as I'm already home and there. If I couldn't possibly manage it then I'd ask DH to do it when he got home.
If you want to do nothing during the day other than looking after the baby then surely it should have been spoken about before as in "once the baby is here, I'm dedicating all my mat leave to nothing but baby duties therefore housework and dinner will fall to you"
It's like night feeds, I did all of those because I didn't have to be alert through the day for work. dS woke and fed every two hours for the first 8 weeks then started on 4 hours and was sleeping 10pm till 6pm from 16 weeks so I slept ok on the nights then.
Again even with not much sleep, I didn't sleep during the day but even now I only get 4/5 hours sleep a night because I'm an awful sleeper anyway.
If your struggling to cope with the new baby and can't do nothing in the house other than care for baby, then you need to tell him. But I found divided households really hard to get my head round anyway but accept that it works for some.
Until I read more posts on here, I didn't realise how family roles are heavily criticised and condemned. Even SAHM are livid that they are expected to tidy and cook yet to me that encompasses the role of staying at home. I wouldn't.mind if it worked both ways but there's definitely double standards in many households on here.