We've had a 13 for 12 years
The bed would be long enough,, barely but it is a narrow bed and the curved corners of the trailer would be a problem for your height.
We are 5'10 and 5'4 average build and it is pretty much full.
Interior height is close to 6'1.
I get ours in and our of the garage that has a 7 ft. door.
but I have to use an old pair of 13 in. rims with no
tires to do it.
Fred