Best way to haul a quad?

Yes, before taking off with your ATV or "quad", you should be very familiar with the laws in the area where you plan to stop.
Here in Montana, in order for your ATV to be street legal, it must have a rear view mirror, a horn, a muffler, hi/lo headlights, a taillight, and a license plate light. An ATV that is NOT street legal can not be ridden on public roads. Numbered Forest Service roads in the back country are considered public roads. You may not ride your ATV cross country where there isn't already a track.
Out of state ATVs must go to any Fish, Wildlife, and Parks office to get a sticker, good for one year, cost $5.
Just some examples of things an ATV owner should know.

To directly answer your question, I don't think there is a safe way to haul a full size quad on an ATV carrier just attached to your existing hitch. I think a quad would be way too heavy to be safe on that type of mount. But as already mentioned there are ways to do it, but it would involve welding and probably a three point attachment to the motorhome to do it safely.

Now other things to consider, I haul my quad in the bed of my Dakota toad. I don't know where you plan to camp, but I would think the vast majority of campgrounds usually prohibit the use of off road vehicles (such as quads) within the campground. There are many campgrounds that specifically do allow the use of quads and they are often adjacent to off road use areas.

If you are not going to pull a towed, pull a small lawn service type trailer (the kind where the tail gate folds down into a loading ramp) for the quad.

Or, better yet pull a small, lightweight pick up as a towed and load the quad on the truck using ramps designed for that service.

Since you are going FT in two months you need to rethink "NO TOAD".:S Yes, not having a toad when FT is a dumb idea and most places will not let you drive the ATV on the road or in most CGs.
We put as many miles on our toad as the MH which increases our overall MPG from 7 to 15. The MH becomes our base camp and the toad is used for sightseeing and getting supplies. Do you really want to pack things up and unhook your utilities to go to a movie or to town? Buy a small PU that can be towed four down and put the ATV in the back of it.
Put a 2x4 across the front of the PU's bed so the rack on the Honda does not hit the back glass before the front wheels stop against something. It's already saved me once when the ramp kicked out and I had to punch it to get in the bed of the PU.
If the above is not enough info, then that much weight that far back is going to overload you rear single axle 40' MH. Click on "How I tow" below for why I say this.

Check out the cricket golf cart. Half the size of a golf cart carries 600lbs, four people, or two with a basket or bed on rear. The unique thing is they disassemble to where they fit in your storage boxes if your boxes are good sized and if you pull a suv it will fit in the rear of them easily.

I use a 12" utility trailer with fold down/up ramp. Trailer is light and hauls my 1200 lb. Honda UTV just fine behind my Motor Home or Truck with Truck Camper.

Here is the safest and easiest way to take your ATV with you. The dual swivel wheel trailer is considered part of the coach and can be backed up with no problems. Check the Yuma craigs list or the local Yuma classifieds, as there is one for sale there for $1700, which is a very good price on one.

We use a 20 ft car trailer with my Polaris RZR loaded sideways at the front and my Honda CRV loaded on the rear. When we are at our destination we have the option of using a tow bar with the CRV. We winter in southern Arizona where riding ATV's is a big attraction. We also have a smaller trailer when we don't need a toad. The trailers are inexpensive when you compare them to the price of those special lifts.:)

We just went through a similar selection process to haul a 900 lb golf car. Your options are Hydralift attached to the back of your coach, a Blue Ox hitch mounted platform, pull a trailer, or get a pickup truck and haul the ATV in the truck.

.Hydralift is expensive but seems to be a sturdy option. Requires some welding on the coach.

.The Blue Ox platform also requires a three point hitch receiver to be welded/bolted to the coach.

We elected to get a F150 and haul the golf car in the bed after considering all the pros and cons of each option.

It it were me and I did not want to have a toad, I would go with a utility trailer.

If a trailer will work, I saw a Triton aluminum trailer that had both sides as swing down ramps so you could just drive them on from the side. great if you have two of them, getting them on crossways.
bumpy