Hi Rachel!
There is a train that does a round trip from Baltimore, MD to Orlando - Amtrak. I recommend that you do a search online for availability and rates to accommodate your schedule and budget.
I am unaware of any special transportation from the Amtrak station in Orlando that will get you to Disney, other than car rentals, taxi, or shuttle, which can all be pre-arranged when you make your reservations.
If you decide to take a flight to Orlando instead, then I suggest you look into Disney's Magical Express, which will transport you straight from the Orlando Airport (MCO) directly to your Disney Resort.
Learn more about Disney's Magical Express by clicking on this link:
Disney's Complimentary Airport Service.
The Magical Express bus is beautiful, clean, exciting, and a wonderful start to your Disney vacation. If you think this is something that your son would enjoy, then I highly recommend it! I have not traveled via Amtrak before, so it is not something I can personally recommend, though I have heard great things about it.
I hope you have a wonderful & magical vacation experience at Walt Disney World!