I'll run the numbers since no one here has actually done that.
Estimated weights:
B2601 - 1632 lbs
FEL - 559 lbs
Bucket - 200 lbs
Backhoe - 750 lbs
Total tractor load - 3,141 lbs - assuming no other implements or ballast (like fluid filled tires).
Trailer weight is 770 lbs - add that to the tractor load. Grand total ~4000 lbs which is less than 5,200 lbs so your trailer can haul it.
Next is tongue weight. For 4000 lbs you want 10-15% tongue weight, let's assume 13%. That's 520 lbs. This means you need to position the tractor on the trailer so that it puts 520 lbs of weight on the truck. With a short trailer and limited space to maneuver you may struggle getting this right.
Next is your truck's capabilities. Look up your truck's payload capacity, should be a sticker on the drivers side door. This is the amount of weight you can put on your truck which includes, people, gear, tongue weight, etc. I have a base model F150 with few features - my payload is 2000 lbs. If your Ram is a high trim model, you'll be surprised how all those comfort features drastically reduce your payload capacity. Add up your body weight, passengers body weights and anything else in the truck or in the bed. Add to that the tongue weight. This total cannot exceed the payload capacity.
Next look at your trucks towing capacity. You might need to figure out if you have a tow package or not and what your truck can do.
I'm assuming your situation will be fine, but the above methodology is the way to answer your question with facts.
BTW congrats on the B2601. I just picked one up myself. Backhoe will be in sometime this month (July).
