Larger
diameter tires should be better for rolling resistance, but larger tire
width is worse.
The Tractor Supply
Carry-On 4 ft. x 8 ft. Trailer, 1500 lbs. GVWR is described on their web site has having "12 in tires rated 990 lbs each". With that capacity at 80 PSI, I'm guessing the tires are what they sell as
Trailer Tire, 4.8 - 12, LRC.
A 4.8" tire has a nominal section width of only 122 mm, but an actual width of as much as 135 mm... if you could get a 135/85R15 tire (which you can't, although you could get close to the size with an unsuitable space-saver spare intended only for temporary use), I believe that the 15" setup would have smoother ride, higher load capacity, and less rolling resistance. You would have to find an unusually narrow 15" wheel in a trailer hub pattern and offset, or use an adapter of some sort.
In a quick search, the narrowest 15" tires I could find in North America from tire companies was a Bridgestone Blizzak LM-18 145/65R15 (a winter tire for passenger cars, Euro-sized). Due to the relatively low profile, it's less than two inches taller overall than the 4.80-12. Among other brands, the Michelin X-Ice 175/65R15 was next narrowest (again only a winter). I suspect either of these would roll pretty nicely, but the ribbing from other trailer owners about the winter treads might be hard to take.
The Smart ForTwo uses a 155/60R15 on the front, which would probably be a really nice trailer tire... although I don't know where you buy those tires other than as the Bridgestone Blizzak (Goodyear, Michelin, Continental... none list the size). The Smart wheels fit a
three-bolt hub.
In Europe, Continental has the
ContiEcoContact 3 in a 135/70R15, which sounds like a nice small trailer size... but only in Europe.