Without giving us the GVWR of the trailer, I would have to guestimate 5120 + 1000 for the loaded trailer weight - 6120 lbs. *12.5% = 765 lbs approx loaded TW.
Then again, your unloaded TW is already 775 lbs (WOW!). So either you have a lot of storage in the rear of the camper (which would offset the battery, LP, etc), or your TW will be much higher than the average 12.5%.
6120 * 15% = 918 lbs. That would have things too close to the limit of a 1,000 lbs WDH system.
So, yes, I think the 12,000/1,200 lbs Equil-i-zer (DC, etc) would do you well. Even if the TW stays down in the 800 lbs range, it's well within the usable range for a 1200 lbs system.
thebrakeman ('70), DW ('71), DD ('99), DD ('01), DD ('05)
2004 Surveyor SV261T (UltraLite Bunkhouse Hybrid)
2006 Mercury Mountaineer V8 AWD Premier
Equal-i-zer WDH (10k), Prodigy Brake Controller