I've seen DIY trailers with 26" wheels. If anything, they'll roll over obstacles easier, like you said. I don't believe there would a problem with larger wheels when cornering. They're meant to carry people after all at much higher speeds.

One thing to keep in mind: watch your center of gravity; the lower, the better. So keep that in mind. With small wheels achieving low center of gravity is easier, depending on your design, of course.