Consider that your F150 with a max tow rating of #8000 assumes you don't have any passengers or load anything else in the truck....
#6000 DRY trailer can be speculative as to what that all includes in that weight, but assume it means that probably not how much it really weighs when you buy it and add a few items to it..
What's the GVWR of that trailer? If it's much over #8000, then you might not like that F150's towing performance, but that's pretty speculative too..
Not saying you can't tow it... Just saying that it'll be a pretty much maxed out load..
When I was a kid, Mom, Dad, me and my little sister camped in a little 14' 1963 Shasta trailer... :) That was a step up from the Army Surplus tent we used before that! Or the little 8' cabover camper we had.. (this was back in the early 70's)
We did move up to a 26' "bunk house" 1977 Taurus travel trailer and that was "Glamping" for sure! ha, ha!
Anyway, enough of my memories... Today is today and you gotta do what you gotta do.. I'd go for something in the GVWR of no more than #7000 on the TT. But, that's just me..
Good luck!
Mitch