Yeah, you will need to bring a few extra gallons. What are you and your dad running? I remember when I was running my '88 Suzuki Samurai (it's pics are in that facebook page) and with its stock 10 gallon tank and a 6 1/2 gallon jerry can on the back, I would leave Lancaster, stop in Mojave (for everyone else to top up as my needle hadn't even moved yet) and wheel for 3 days and 2 nights out there not having to get gas til Mojave on the way home! lol. Sadly, with my Cherokee, those 28-32 mpg days are gone haha.
I will recommend the usual items...
1. Bedding (depending on your sleeping arrangements)
2. Food for however many days you plan on hanging out
3. Water for the same~in summer I bring a gallon a day for me to drink and wash and a couple gallons for the rig just in case.
4. Please bring a little firewood, I try to get everyone coming to do this as it makes it easier for the group as a whole
5. For dinner, it depends on the group and personal desire. Tho we quite often all pitch in and share making a big ol BBQ out of it. But, no worries, just whatever works.
Those are just the basics. Being you (and I presume your dad) are both on this site, you likely have plenty of smarts when camping, off roading, etc.
Again, look forward to meeting you AND your dad and anyone else we can get to go on this trip.