Congratulations on your "new" Scamp
One thing to look for before changing to a larger tire is how much clearance you have between the top of the current tire and the inside of the wheel well. You'll want to be able to put your fist in this gap (room for at least a 3-inch "bounce" of the axle). A 14" tire is considerably taller than the 13" tire; so you may have enough room for the 13", but not enough for the 14". You may have to have a spacer added between the axle
and the frame to give enough clearance for the larger tire (there are some good shops around that can do this...Salem Brake and Wheel in Salem does great work and makes sure that the axle
is properly aligned).
I applaud you for wanting to make sure you have good tires
for the ride home. We picked up our first trailer in S. California and had a tire blow out on the way back because the trailer had been stored too long. The tires looked new, but the storage had created a weak spot. This blew a hole in the bottom of the trailer that I was able to repair, but it was no fun.