If you have the 5.3L/6spd/3.42 axle, then I'd try it. Just consider what you would do if you are not comfortable with the setup. Are you willing to replace the Tahoe next month? There really are not many SUVs with more capability than you have already. Are you willing to get a pickup or full sized VAN? Basically, you want to formulate the backup plan. If you do not have one, then you may not want to change what you are already happy with.
A 5-week trip means a lot of stuff. I expect you'll be traveling right at 8k pounds with that new RV.
