Gary, Your new inverter is likely the 1800 watt model, but double check your inverter's paperwork in the gray vinyl bag. On the bottom of the crock pot, it states the wattage. Our small crock pot at home is rated at 100 watts, and our large one is 250 watts. Based on this data, I would say it is very safe to do as you are considering, especially if using a small 100 watt crock pot. Understand that you wouldn't want to opperate off the batteries alone for too long a period, but you should do well driving along on the open road. The chassis alternator should supply more than enough power to cook with a crock pot.
The first time you cook while driving, pay very close attention to the dash board instruments. If your battery needle jumps and stays low, then I am surely wrong. But I do think you'll be just fine. Just don't use a monster power hog crock pot model that feeds a boy scout troop.
Keep in-mind that you may also want to watch a movie with surround sound when on the open road while the crock pot is on. So the smaller the crock pot, the better. You don't want to limit yourself if you can avoid it.