It is much better to use larger diameter tube with a thinner wall, than smaller tube with a thick wall. In the end, the result is more strength per pound. 1"x1"x 0.125 (as suggested above) may be strong enough for the task, but it's going to be a heavy pig. I would suggest shopping for tubing that is at least 1.250" diameter, with a thinner wall, maybe in the 0.080" range.
That said, frame design plays a significant part in tubing selection. A ladder frame (as I assume you're building requires beefier tube than a triangulated space frame. A decent space frame can be built from 1" x 0.065", whereas a ladder frame of the same material would fold like a cheap suit over the first bump.