Powerbuilt Unijack 4,000 Lb.

The only time I needed a jack when I was on the road was a camping trip at Hope Valley, CA, where I discovered that I had burnt up a bearing on the left wheel.  It was parked on an uneven surface, next to a log laying on the ground, in soft dirt.  I had no problem setting up the bottle jack and accessing it.  Had I tried to use my floor jack, it would have been almost impossible to get it into position, stabilize in the soft ground, and pump it with the log blocking access to reach the long handle under the trailer.

Both the jack that StephenH suggested and the low profile jack from Home Depot are good choices.  They have about the same unextended height [5 5/16" vs. 5 1/2"], both are lighter than a floor jack [18.3 lbs. vs. 25 lbs.], and both have adequate capacity [2 tons vs. 12 tons].  The bottle jack costs a little more, but takes up a lot less space.  The big difference to me is access to the handle and ease of pumping it.  The bottle jack is easy to pump from an accessible position.  The trolly jack, in order to be positioned under the axle lift point, must be in a position that makes it harder to reach the pump handle.  If it requires a lot of force while pumping [as was the case with my floor jack], then it could be a bit more difficult to use.

Our current trailer, like Dave and Dannete's, has leaf springs, so we don't need a super low profile.  The bottle jack I use has about 6" of unextended height and works quite nicely with a piece of 2x6 under it.  I wouldn't even think about using a floor jack, or anything with wheels where we currently park our trailer.  It'd sink right into the soft dirt where grass used to grow.

I would be very cautious about using a bottle jack due to risk of sliding like that, and advise never jacking a trailer unless it is hitched to the tow vehicle and the opposite wheel was chocked.

As for bending an F150 jack lifting a small travel trailer, it's hard to imagine  how that would happen. An rpod axle fully loaded only weighs about 2000 lbs so any jack with a 1.5 ton capacity or higher should be fine.