I think your VW is probably rated to tow less than even a 13ft fiberglass RV would weigh with gear in it. You might want to take the $5,000 for a camper and the sale price of the VW to arrive at what you have to spend on the whole rig. Tow and trailer.
Smaller the tow vehicle the more important trailer brakes become. Can tow does not mean can stop.
Try to get to a FGRV rally
and check out the rigs to get an idea of what would work for your needs.
Rallies, Get-togethers, Molded Meets (Upcoming) - Fiberglass RV
To get an idea of prices see this part of the forum for rigs for sale
For Sale: Molded Fiberglass Travel Trailers - Fiberglass RV
In the 13ft size there are many under your budget, and yes if it is older it may be in "working" order but need work to be dependable or fully functional.
suspension being worn out, floor rot, propane fridge
, and furnace
are probably most expensive issues with older trailers. Assuming the camper does not currently leak and appears solid and in good repair.
can be hidden and create wood rot out of sight under a cupboard or seat so be sure to check the wood floor condition. From inside and under the trailer.
Allow for the nickle and dime stuff like window seals, or battery(s) for the 12 volt system you need when not plugged in. And if you can plug in for electric service the campground cost more than a rustic campground with pit toilet and hand pump and no electicity.
Heat for the lizard is going to be a bigger problem than the dog unless it's a really big dog. Heat from electricity draws a lot of power, so your camper batteries will get a heavy drain if you try to heat a lizard cage. Or your paying for a campground with electric hook-up.
We can get two people and a 40 lb dog in for the night in a 13ft Scamp
but I think it would get old if the three of us were stuck in there for a few days.
Most campgrounds won't let you leave a dog unattended in a camper. If it's hot where you camp you may need/want air conditioning
, if not for you then for the dog. AC can be expensive to fix and requires plug-in power from campground or a noisy generator
, not going to run off of batteries.
If your going to need work table and bed be aware that many 13 ft eggs use the dining table as the bed. A single person might be able to set up bed on the couch/bunk and leave the table up for eating or working. Or some models have a second dinette table for two. Either from the factory or added by the owners in place of the couch or a closet.
If the camper does not have a bathroom there are places one can stow a port-a-potti. These are pretty easy to operate and empty in a rest area or campground toilet. This would allow you a bit more flexibility in where you spend the night when traveling or camp for a few nights.
Someone mentioned sponge baths, yep been there done that. Used an 8 cup coffee pot to heat the water. Never tried to shampoo hair inside the camper but have done that outside.
As if my post was not long enough already....
A screen tent or pop-up canopy, especially one with side panels to keep the wind and wind driven rain out can really "expand" your living space. A 10 x 10 canopy is bigger than my 13ft scamp
Throw in a portable camp stove and maybe a lantern so you can cook, eat, and work in the canopy or screen tent will greatly enhance your camping experience.
If you pull into a camping place and it's raining or your only staying one night your camper is ready and waiting. No need to fuss with the extra screen tent or canopy. Otherwise you can set up outside and double your space and comfort.