Breast feeding is recommended by the WHO until at least aged 2, for the benefit of the child. It's not a 'choice', if OP can breast feed, and wants to breast feed, that relationship should not be severed for the wants of a man.
No court will give overnights this young.
Allowing him to have contact little and often, in a place baby is comfortable, to ensure baby's needs are met, is what a court will order.
Courts will start to look at overnight contact from age two, with a dad who has done the little and often in the early days.
Soon, the baby will go longer between feeds. He should be able to take her out for an hour or so just now, most babies are going an hour between feeds at this age.
Mediation sounds a really good idea, and the courts will want you to have tried it.
It's going to be far better for the baby if you can work together through mediation. I'm sorry, but you are going to have to allow more contact than your current plan, it's great he wants to be involved.