I have the same GMC truck 04 2500HD 4.10 4x4 . I would upgrade the 04's stock recvr. hitch. They were 'not the best' .
My non slide Lance 845 camper is about 4000# and i have been towing boats and various trailers for 70k miles with this truck, no issues.
Trailer: Cargo Pro (Sno Pro) 5x12 alum. 950# dry wt. loaded up=2000# , which is under the payload of the 3000# trailer. AS for the truck , i'm under the rear axle wt. but over my GVWR of my truck because of the camper . I'm ok as far as the combined weight . Im not worried about the GVWR because the trucks frame can handle it, the axle rating is what's important, that's the weak link.
I did upgrade my tires to 265x16 E in order to beef up the low 6000# plus rear axle as stated. With the new tires my axle is now 6800# plus. (these are rounded off numbers by a few lbs.)
to offer better control and handling I added Rancho 9000 shocks, rear sway bar, air bags and stableloads. I also added a CURT 2.5" hitch with a 24" extension because of my campers overhang.
CURT 2.5" hitch Tongue/hitch wt. should be 10-15% of the trailers wt.