Hi, S.. Well, if it's taking her longer to fall asleep in the new bed, what I'd do is to try to get her more tired out before bedtime for at least a week. Also, since she can't tell time yet, move her bedtime up an hour. In other words, if you usually put her to sleep at 8, start bedtime at 7. If she takes a very long time to feel comfortable enough to sleep in what is a strange bed, then give her a head start.
You might also spend some time with her in the bed when it's not bedtime, just to get her used to the new piece of furniture. Maybe practice putting her dollies to bed in the new bed, showing her how comfortable and safe her "big girl" dollies are.
Peace,
Syl