Hopefully you can discuss it in a reasonably amicable way. While your daughter is so young it might be better for her to be in her own environment at first, but it is fraught with difficulty if there is tension between you. I would move as swiftly as possible to perhaps him taking her one afternoon a weekend, then move to the whole day. But overnight at 14 months would certainly have been too young for my DD, but they're all different and you'll know when yours is ready.
Are you and your OH very far apart in terms of what you both expect? Does he actually want her overnight at the moment?
I think for an infant, one day every weekend is a pretty good arrangement, and perhaps a visit during the week. The difficulty is you can't plan anything (such as an evening class) unless he is going to be reliable and agrees to a routine. When you are confident she can do overnights you could then think about moving to every other weekend.
Bear in mind too that in a couple of years she will be starting school, which can be pretty exhausting for them initially, but also requires an earlier pick-up and later drop-off. Will your OH be able to do that around his working hours?
My friend, whose ex started out demanding "his rights" etc, finds she has to be available to pick up the slack in terms of childcare just as she did when they were together - two years on from separation. Despite telling her she should go out and get a better paid job (she's a childminder) he makes full use of the fact that she works at home to change arrangements at the drop of a hat, knowing she is always able to step in. He's also found that the OW isn't quite as accommodating as he imagined she would be in terms of childcare - so the initial demands to have the children 50-50 became more subdued as he eventually realised it just couldn't be done.
Don't torture yourself thinking about junk food etc at the moment. It might put your mind at ease if you pack an insulated lunch bag for her perhaps?