Yes, you should have little problem hauling this load.
Golf carts are 42 inches wide (measure one) but you will want at least 50 inches to have room to maneuver. My Honda quad happens to be the same width. I haul it beside a Harley bagger almost every time we go out. The Harley is dressed too, I don't strip anything off to haul it.
I have placed the floor bracket for a Condor bike stand on the left side of the garage. The bike sets close to the wall so getting to the tie downs is not easy. Then I drive the quad along the right side of the garage and tie it down. My hauler has 9 tie downs welded to the frame and can take 2500 lb. load each. Once both toys are loaded I can still get around in the garage but it is tight.
When I did the first set-up I did some measurements and then set the Condor where I guessed it should be. Then I drove the bike in and then the quad. Once I was happy with things I marked the floor for the bracket and unloaded. After I put the bracket in I can just carry the Condor out and mount it to the bracket and the toys go in the same every time!!!
For what it's worth - - an electric golf cart weighs about 900 lbs. Gas power is lighter but not much. Your Bagger weighs about 900 lbs. too. As you can see, you should be under your camper's ratings pretty good.
I roll the carpet from the garage floor up and place it between the toys to travel. This is a secondary barrier to keep the toys from sliding into each other. I have other stuff that travels in the garage with the toys too.
If your Hauler has a dove tail entrance to the garage, drive your bike just onto the flat area when you tie it down. Leave it in 1st gear and use a bike stand if you can get one. Condors are not cheap but after paying for a new Hauler - - what's another $200 anyway?? Most Harley dealers sell them. If you go to a large rally, the Condor company usually has a vender tent and sell the trailer models for $150.
I have the floor bracket mounted in my hauler but use the Condor in my house garage when at home. I can get two cars, a motorcycle and a quad inside a two car garage easily and have access to them all by just parking my Harley "upright" in a stand!!! If you have a Harley and a Toy Hauler, , you should have a Condor (or similar) stand.
Don't skimp when you buy tie down straps. Buy 4 for the cart and 6 for the hog. Take your time and get the load laid out correctly and secured and you will not have any problems hauling your toys.