The 26BH is a great first trailer. It will be tight in the middle and as the kids grow it will get tighter, especially in the dinette. Also, you will have little privacy in the bedroom area, although if your kids are little this won't be a problem.
A trailer with a slide will provide a lot more space without adding all that much weight.
Your truck will be good for a trailer up to GVWR of 7500#.
And has been previously stated, the CAT Scale is your friend.
Welcome to the forum!
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