Welcome to the forum, Nicole!
Borrego Dave is correct. Molded fiberglass travel trailers- at least the kind you can stand up in- all weigh well over 1000 pounds even minimally loaded. I've seen a number of ads claiming 800 or 900 pounds. Those are dry weights- they don't include the appliances, propane
tanks, batteries, or any of your stuff- and they're suspect even then. A gutted, empty shell, maybe.
A teardrop is within the realm of possibility, but even then, some larger units that have complete kitchens on the back, AC, TV and stereo,... can get surprisingly heavy.
The American Outbacker teardrop has been mentioned here a few times, but not often. I vaguely recall it is plastic, not fiberglass, but I could be wrong. Not many made, I think.
You might set up a Craigslist search for teardrops. Occasionally I see simple home-built units for sale
, often quite inexpensive. It won't be molded fiberglass, of course, but it will give you a dry, secure place to sleep off the ground.
A motorcycle trailer is another possibility, but they usually have canvas and fold out. Don't know how that would stand up in the Mojave Desert- it can get pretty windy.
Remember to allow for your stuff. The lighter and more basic the trailer, the more extra camping gear you'll have to bring along. I would be looking for something under 500 pounds, so you can add your clothes, food, and gear without overloading your vehicle.
How about a used van instead, and leave your nice Elantra at home? It doesn't have to be a full camper van as long as it has a fold out bed. I camped for a few years in a hand-me-down travel van. Unlike a teardrop, you can invite a friend or two inside...