Hi Diana!
Welcome back to the Disney Parks Moms Panel!
I believe I just answered your question about the
Minnie Van Service at Walt Disney World Resort. I do think that service (or regular Lyft, Uber or taxi) will be your quickest way to travel from Disney's Port Orleans Resort to Disney's Contemporary Resort for your reservation. Regular Lyft and Uber would probably be less expensive than the Minnie Van, but not nearly as magical!
My other suggestion for travel would be for you to take the
Walt Disney World Bus Service to Magic Kingdom Park, and then walk to the Contemporary Resort for your reservation. If you choose this option, I would allow at least an hour and a half of travel time.
If you end up taking a vehicle, you could take your luggage with you. However, when you hop from one resort to another, you can actually leave your bags at your first resort (at the Bell Service desk) and they will transport them to your next resort for you. We used this service on our last trip and it was very convenient. Just know that you probably won't receive your bags at your new resort until later in the afternoon hours.
I hope this helps! Please let me know if you have any other questions.