We bought DD "adult" furniture when she was just 4-5. I decided I didn't want to have to buy furniture more than once so we got her a queen size bed, 5' dresser, and matching bedside table. Everything is solid wood, so not going to be falling over. She can get things out just fine.

We just got the IKEA Nornas Dresser for DS. I like it because it comes with two cubbies for storage.