Your Navy base should have a great MWR Recreational Services and perhaps you can check out a small trailer. Even DOD folks can use the MWR tiems. Here at Dahlgren VA they have a couple of campers available. Most bases also have a set aside camp ground somewhere too... The one for this base is at PAX RIVER...
Might give you a good idea how big a trailer your SUV will like to tow and be safe.
I'm thinking anything over 24-26 feet is going to be your maximum for safe towing... Your 34 foot trailer will want a minimum F250 and probably a F350 would be better. Its not all just the weight it is the wind load as well to consider. Try passing a over-sized log truck coming at you at 70MPH on a two lane road with you pulling a high trailer and see how that works out... The last you may remember is the driver with a big smile on his face haha... Been there done that a couple of times - me loves Gerogia Pacific trucks in Arkansas on US82...
My 28-foot fifth wheel that the salesman said your F150 truck will pull this baby with ease still sits in my back yard setup as a get-away place for us and the grand kids... We pull a 4000 lbs loaded OFF-ROAD POPUP trailer with our F150 all over the East and South areas from here in Virginia...
For us however it is all about RV CAMPING not RV TRAVELING. That a whole different ball game and a really bigger expense...
Roy Ken