Single Cab "3/4 ton" will be fine. 4x4 CrewCab and he will be over the ratings. Will it do it, without a doubt any of the three 3/4 ton trucks will tow it. Will it do it and be with the payload/GVWR, that will depend on cab config and powertrain.
Also, since the OP is already showing the signs of upgrade-itis, and my personal experience is that that disease is hard to cure, going to the 1 ton would ensure at least 1 round of trailer upgrades without issue, HA!
Current TV:'14 F350 Lariat CrewCab, 4x4 Short Bed SRW Diesel w/ Pullrite 2700 (16K)
Current Fiver: '15 Puma 295BHSS Anniversary Edition
Past TV: '13 F150 HD Payload SCrew EB, '08 Tundra CrewMax 5.7L, '02 'Burb 5.3L, '97 Dakota 3.9L
Past Trailers: '09 Wildwood LE 27RB, '02 Palomino Yearling RL, '87 Jayco 1006dlx