Sarah, welcome to the forums! Please be assured that not everyone who posts here is grumpy -- some of us try to be as helpful as possible. Don't be discouraged!
Having said that, you really are pushing the limits of what you can tow safely with that vehicle. Most folks like to build in a big cushion of safety. The issue is not towing on flat ground. It is going uphill and (more crucially) downhill.
Coming from LA to the Kern, you will have to deal with the Grapevine. Up the hill northbound, you will be in the truck lane. Just be patient, and watch your engine temp.
Coming down the hill northbound is a little trickier. You will definitely want to downshift to save your brakes from overheating. That particular stretch of road is tricky because we tend to go faster than the trucks and slower than the cars, yet there are only three lanes on that downgrade.
On level ground in the San Joaquin Valley, keep your speed in the high 50s.
Will this rental come equipped with any sort of sway control? If not, be sure to load the trailer heavily in front of the axle -- inadequate tongue weight can cause sway, which can get very dangerous very fast.
Once you decide to buy a trailer, you may want to look at a beefier tow vehicle. I tow a small (2000 pound) trailer with a Tacoma, supposedly rated at 6000 pounds. It is sufficient.
Don't be discouraged by all of the technical stuff connected with towing and trailering. Yes, there is a steep learning curve. But it is incredibly fun, and great for folks with kids. We did not discover camping till our kids were grown, unfortunately. And living in California means that although the traffic is bad, there are lots and lots of places to go, all year round. Check out our blog posts (see link in my signature) for a taste of what is available to you!
Unless I am mistaken, I think it cools down on the Kern after sunset. So although you will need the a/c for the baby's afternoon nap, you might not need it at night. Hybrids have much better ventilation than hard-sided trailers (like mine), which is both a plus and a minus.
Hang in there, and have fun!
2012 Fun Finder X-139 "Boondock Style" (axle-flipped and extra insulation)
2013 Toyota Tacoma Off-Road (semi-beefy tires and components)
Our trips -- pix and textAbout our trailer"A journey of a thousand miles begins with a single list."