That trailer's a long bugger, isn't it?
Looking at the specs, it shows a tongue weight of only 405 lbs which is less than 10% of the trailer dry weight of 4150. You may need to load the front up a little bit, but then the full propane and the batteries could help.
I know tomhole here has A LOT of experience with this and can help you out a ton.
For your tundra, this weight is NO problem whatsoever. I towed a 23' Terry TT a few years ago with my 02 tundra and 4 speed auto (not 5 sp. like yours), and it did great. That trailer had a dry weight of 3900lbs.
A few things you'll want to address:
Get a good brake controller like a prodigy P-3 or prodigy. Don't mess with the cheapo's.
Does your truck have LT tires or just the P Rated OEM ones? It is recomended to run a C or D rated tire when towing, and air them close to max psi cold.
Maintenance is MORE important when you're towing than not. Be sure to follow the maintenance guide to a Tee for severe service or what's recomended 'while towing'. Diff fluids are very important here, as well as coolant, trans fluid, and greasing the u-joints. You may want to address these issues before you venture out.
Any more questions?
Those dam RV shows anyway; they always make you spend more money.