Inverter wiring

I inadvertently posted this in the wrong forum as I have a motor home but you guys have given me good info that works for whatever vehicle. The reason that I am looking to upgrade to 2000 watts is for 2 short term uses. The first is for a hair dryer the second is for a coffee pot. Either would be "on" for about 5 minutes so if the inverter is connected to two 6-volt Trojans and it is only operating off the battery in 5 minute increments, will I have enough juice to get the 5 minute job done?

We camp a lot in Calif State Parks and often times they won't allow a generator until 10am. Crazy, huh? That's why I'm looking for something with a 1500 watt short term output.

Thanks