Welcome to the forum. As you can see in my signature I have a Tundra and a WH which has a GVW of #7500.
When fully loaded the trailer weight is about #6800 and hitch weight is about #900.
My payload is maxed out, however the Tundra handles this trailer just fine.
To be clear; #5900 on trailer axles and #900 on hitch. I would not pull a heavier trailer with this truck.
That being said, I love this truck (it has a bed cap on it which adds about #250 to its weight), which reduces its payload by that amount. I have DW and #100 lb black Lab as regular passengers. I will keep this truck until either I or it drops dead. Also this will be my trailer for a long time.
From what I have read many CA state parks have minimal facilities and severe restriction on length -20 feet or so.
Don't get something too small or your family will not be comfortable. So consider all of your camp site options.
Good luck with your search!
2012 Toyota Tundra 5.7 Litre DoubleCab
6 speed, 4.30 Limited Slip, Tow Package
2013 Jayco White Hawk 27DSRL
2010 Jayco JayFlight 26BH sold
Yamaha EF2000is Generators (2)
1996 Honda CB750 Nighthawk