We weren't in a hurry when we made the switch so I spent the first few days asking DS where he wanted to sleep. Most times he chose the big bed
We made a big deal of how exciting the new room and big bed were and every time someone came to visit we would get DS to go and show off his bed and they would 'ooh' and 'aah' etc! This really worked and only took a few days for him to happily have both his naps and nighttime sleeps in the new bed. Maybe we were just lucky? Most nights, after a few stories and songs he goes off to sleep by himself. Occasionally I have to sit in there with him but I ALWAYS leave before he falls asleep and he knows the door will be closed if he gets out of bed (mind you, my DS is a little older than your DD). Good luck, it must be hard doing it on your own most of the time.