I don't think they will transfer them to a new card BUT you can go to disney shopping.com and buy a gift card. That is what I do and then you don't have to worry about the $ expiring. Be advised that when you do this, they do ask for a credit card info, but they use your rewards cards dollars first.
For example, you have 39 dollars on your rewards card. You purchase a $$40 gift card. They will use the $39 from your rewards card first and then charge your credit card the remaining $1.