My experience with a similar rig, weight wise is that you can do it, if you beef up the rear a bit and carry NOTHING in the truck. BUT it is a bit to much. I went smaller and lighter and happier.
If you really need a unit that big, and can't get the right tow vehicle then you can do it, but better hope you don't get stopped or have to stop it in a short space.
As said here, many do do it.
2007 Chevy 2500HD Classic LBZ Duramax/Allison (Stock)
2005 Bigfoot 1500C8.2 AWESOME