you are not moving her to early. my daughter did the same thing at just about the same age. i found a toddler bed for her. this type of bed takes the crib mattress and puts it on a frame that is like 18 inches off the ground. she can stand up from it and not fall out. it also has a partial rail for up by the head and torso area to help keep little one in bed. also because the sheets stay the same - it's more comfortable for the little one. this lasts until they are like 4 and then they have to move to a twin bed because they are too big for the crib mattress.
when you move her, tell her she is a big girl now and doesn't need her baby bed any more. tell her how proud you are of her and how exciting it is to be a big girl. you are going to have to work at teaching her to stay in her room after you put her to bed.
if bed time is 8, you may not be able to go to bed until 9 - after you make sure she is asleep. as for wandering in the morning - if you know she gets up at 9, you may need to get up at 8:30 so you are ready for her...
i had an interesting time moving my children, but it took time and patience and they learned to love the "big kid" bed. a note of encouragement - the transition for the toddler bed to a twin bed is much easier....