Hi Rachel and welcome to the Disney Parks Moms Panel!
You are so lucky to have gotten one of the coveted tickets to Passholder Play Time in
Toy Story Land! I think you'll love the new attractions! If you're hoping to hop over to Magic Kingdom Park you might find your car to be the quickest method.
There is a bus from Disney's Hollywood Studios to the Magic Kingdom Park but I'm not sure how frequently it runs in the mornings. You could take a bus to
Disney's Contemporary Resort and walk over to the Magic Kingdom Park. The walk doesn't take long at all and you would avoid having to use parking lot trams.
Disney's Minnie Van Service is a fun way to get from place-to-place in Walt Disney World but you might have to wait for a short time and there is the cost associated with it to consider.
If I were you, I would drive my own car or take the bus to Disney's Contemporary Resort. I hope whichever method you choose that you have an awesome morning at Toy Story Land and a delightful day at Magic Kingdom Park.
Rachel, thanks for visiting us with your question! I hope you'll let us know if we can help you with any other questions.
Wishing you a magical vacation,
Amy H.