I think both Protege and SolidGold are right here, in different ways.
My Ex left me when DS was 6 months old, and we very quickly (within a month) worked our way up to overnight contact. He now has him every other weekend.
We did this because Protege is right, it is important for kids to have both parents, as equally involved as possible, (in my case I would like Ed to be more involved but he chooses not to) and overnights is part of this.
However, given the concerns you have laid about the situation before he left ect, I would advise building up slowly. I would suggest you talk to Ex and say that overnights for one so young is quite a big step and suggest you build up the time he spends with DC in the day, before moving to overnight.
As you have concerns, I would, as SoldGold suggests, keep a diary and keep an eye on what is happening as you gradually increase the time. It should be very telling given if you increase it to, say, 8 hours in a day he will have to feed and change baby.
You do need to trust your Ex to be a Dad and give him the opportunity to be one, you also need to ensure you are doing it in such a way that you are looking at for your baby and doing what is right for her.
It is absolutely right that your baby should get proper time with Dad, but building gradually and keeping a close eye is also important.
Say no, not just yet, but offer to increase time over the next few months and build up to that.