In my case I used the tongue jack of the trailer I was towing in conjunction with the 2-1/2 ton floor jack I keep in said trailer to change the flat I had a few years back.
The axle holds up the weight the rest of the time, a flat tire doesn't change that. There is absolutely no reason to jack the camper separately if you have a jack that can do the job. To that end I suggest dedicating some storage space to a quality 8-12 ton bottle jack.