Any residential toilet is fine, which will require water to flush correctly. The waste line to your sewer, cesspool, or septic system, will have to be pitched per the plumbing and building codes, and the distance of the horizontal run is of course one important factor.
In a sense you don't have a "trailer" in your yard, you have a "guest cottage" with an aluminum structure and skin.
A composting toilet would work too, but that solution is just as labor intensive to maintain/empty, as it would be in a real road-worthy Airstream.
Your choice, but the first suggestion above is much simpler over time [IMO], if your location permits it. It does, however, raise various zoning and building code issues, which you might want to steer clear of . . .