What size is the tire? The big box stores sell wheels and tires for trailers already mounted or go to a tire store and ask them if they can order you a rim to match yours, plus sell you a trailer tire.
I'm looking to get a spare tire for my camper. Any suggestions on where to look and what I should pay?
The answer depends on whats on your trailer now. You will not be able to run the spare tire on the trailer for far if it is not the same type as whats on it now. ST (trailer tires) are the most common found on our small trailers, with many running a radial.
It would be a very bad idea to go to a 12" tire for at least two reasons:
1. The wheel will have to turn faster and is harder on the wheel bearings
2. 13" Tires barely have enough support for your trailer, 12" will have even less.