It sounds like he thinks she's a object he half owns or parenting is done optionally/in bits and pieces.. it's obviously not, its 100% of the time from the day they're born. You don't just walk out and pop back at 3.5 months old, then walk out for 3 weeks a few months later.
He's been a massively shit partner, but that's not the problem here. He's been a terrible, part time dad for a huge chunk of her life... And now, despite having never been involved or proven he can cope practically, he wants 50/50..? What planet ishe on?
Do what's right for your dd, op. Encourage a safe, rational, slowly built relationship.
For starters he's going to need to know how she's doing weaning. About getting a baby proof space & cot & nappy, wipe, supplies. How teething is going. And that's just basic shit which I suspect he's totally ignorant of... In short, he isn't a fit carer overnight right now.
Your suggestion about building it up over time is excellent.. get him involved in the boring reality of being a 24/7 parent and he may step up.. or be off like a shot 
One tip: from a legal pov, make it clear you're trying to build the relationship slowly but do NOT get conned into agreeing a rigid, set custody routine that may work for him but that a court may enforce later legally because it's a routine that she's used to. I've seen a friend agree to e.g. every Saturday & Sunday with the other parent, because she was on mat leave,six months later, parenting relationship broken down... Court decides this arrangement is working so much harder to deal with! Don't agree to sacrifice your own needs and establish a stable primary care environment to enable him short term, because a court (if it ever got there) might see it as the status quo. And they (rightly) consider what's best for the child.