Would this car be able to handle more than 1000 lbs?

You should ask this question in the alt.rv.pop-up-trailers group.  I
sense that you won't like the answers you get there, however.  It is
not safe to tow above the manufacturer's tow rating because the
vehicle will likely not handle safely, both in terms of manuvering and
braking.  Most experienced tow drivers keep the trailer weight below
75% of the recommended max.  Remember that it is not only your own
safety, and that of your family that is as stake, but also the safety
of those in the cars near you if you loose control.  

Safety aside, the weak link in most vehicles, when used for towing, is
the transmission.  It is very easy to overheat an automatic with a
trailer because the torque converter stays unlocked more of the time,
and even vehicles designed for towing often don't provide sufficient
transmission cooling.  With a manual, it is very easy to burn out the
clutch, especially during low speed manuvering.  

A lot depends on where you want to tow and how far.  If you live in
flat-land and only want to hop over to the state park 40 miles away,
you can get away with a lot more than if you plan to drive through the
Rockies.  We recently gave up our Plymuoth Voyager in favor of a Chevy
Astro; while the Voyager towed our 2000 pound pop-up fine on flat
ground, the transmission would easily overheat in the Appalachian and
Adirondack mountains.  We took the Astro to the Rockies this year and
only had to stop twice, in unusual circumstances, due to excessive
transmission temperature (guage installed).  I would never consider
towing with my SW2, except something small like a log splitter.

I you are mainly interested in a tent off the ground, and don't have
kids, then there are various popups made for motor cycles.  They sleep
two, and have a small space to stand up in to dress.  I have seen
these used by people with small cars.

Thanks for the information.

Please read.

http://www.sherline.com/lmbook.htm