That would be a 1000 watt generator, not 1000 or 2000 kw. 2000 kw is 2 million watts!
A typical tent camper has a 15 or 20 amp shore power cord, so that sets the limit for its power consumption. 20 amps @ 120v = 2400 watts, so that's the maximum power load. However, that provides power to a couple standard wall outlets too - the camper itself probably uses no more than about 250-300 watts to power its 12vdc components. Sooo, the question becomes "Do you ever plug 120vac appliances into the camper's wall outlets?" Computer? Coffee pot? Hair dryer? If the answer is no, or you do without those things when dry-camping, then a 1000 watt inverter-type generator is plenty. Honda & Yamaha make the best, e.g. the Honda eu1000i, but the others mentioned above will do fine too. But if you want to be able to use high wattage appliances like an electric coffee pot or a hair dryer, then you want a 2000-2400 watt model. Yamaha makes a nice 2400 watt unit that would be dandy.
http://www.electricgeneratorsdirect.com/Yamaha-EF2400ISHC-Portable-Generator/p4433.html
http://www.electricgeneratorsdirect.com/Honda-EU1000IKC-Portable-Generator/p6548.html
http://www.electricgeneratorsdirect.com/Generac-5792-Portable-Generator/p3427.html
As an alternative, why not just increase your battery size or carry an extra battery? And get a battery designed for deep cycle use rather than the usual car or marine type battery found in most small campers. With their limited power needs, a decent battery or two should easily last 3-4 days. A group 27 size deep cycle battery will provide about 35% more power than the Group 24 size you probably now have. And carrying a spare would double that again. If you have room, you could move up to a Group 29 size for even more power, or maybe fit in two 6v golf cart batteries, which should last you for several days.