This is one of those cases where everyone assumes the floor holds up the walls when actually the reverse is true - the floor will be supported by the sidewalls and the sidewalls will be supported by the front and back walls - or the front wall and the galley bulkhead, if you're building a conventional teardrop.
So if you were building a fixed body, I would say that you don't need any floor framing and indeed that is exactly what George Teague did when he built his
Compact GT (though that is a 5x8 rather than 6x8). He did add some angle brackets either side of the HF frame but they had all the strength of a pat of butter - here's a couple of photos of his build in progress.
Of course, you want to have a removable body and that changes the picture for your trailer quite a lot - you may end up putting it down on an uneven surface, so 2x2 framing seems sensible. There's no point using 4x2 with a notch cut out at the frame as that's where you need the strength, so it would be little better than a 2x2.
Andrew