Does he have a suitable place that she would be able to stay? Is it set up for a young child - stairgates, cupboard locks, chemicals out of reach... Does he have age appropriate toys, feeding utensils etc? If he has a safe envirnoment for her then that is the first step.
Assuming he does then I would suggest you start by saying you want to see some reliability and consistancy in his contact before you agree to overnights. Saying he wants it is one thing, meaning it and doing it is another.
Perhaps suggest increased building up to overnight. So up it to 4 hours, for the next three months. If he manages to do that then up contact to 6 hours for another 3 months. Perhaps include a midweek time too for a couple of hours.
When that is going well, then you can move to overnights. He could perhaps pick her up on the friday have her overnight and then bring her back saturday evening. That way you get some weekend time as well.
If you are worried that he doesn't know how to deal with the practicalities of beinga parent then suggest he attend a parenting course. All these things will help your case for small steps leading to overnights should it go to court.
If he is serious then he should be willing to compromise and moving from three hours to overnights in 6 months time is a perfectly reasonable timetable.
Good luck and I hope the mediation manages to help you find a solution together. Court should only be a last resort.
Gilly