Hi, Noelle! Thanks for visiting the Disney Parks Moms Panel. As a fellow mother of a tall child, I understand your concern completely!
My daughter has always been a thrill-seeker, so when she hit the 40" mark, she was first in line at Splash Mountain! However, she was a bit older than your daughter at that time. While it's safe for anyone to ride an attraction for which they meet the height requirement, you know your child best and how they might react in certain situations.
There are a few attractions that I think are great options to introduce little ones to thrill rides. First is
Gadget's Go Coaster in Mickey's Toontown. This attraction only has a 35" height requirement and is perfect for a child's first roller coaster. With a few small drops, turns, and a somewhat fast pace, you will be able to gauge your and your child's comfort level with this type of attraction.
Star Tours - The Adventures Continue has a 40" height requirement and I think is tame enough for young children. While it does bounce you around a bit, there are no sharp curves or large drops. Soarin' Around the World might be another great option for your daughter.
If these attractions bring nothing but glee to your daughter's face, she might be able to ride Big Thunder Mountain Railroad, Splash Mountain, and Radiator Springs Racers. For Big Thunder Mountain Railroad, you can usually fit a child between two adults in one row if that makes you more comfortable. On Splash Mountain, you can sit with your daughter in the very back seat. I still like to hold on to my child as we plummet down five stories into the briar patch!
I can provide more specific information if you have questions about a particular attraction, so please stop by again. Have a magical day!
-Linda M.