As is frequently the case, the limiting factor will be the payload capacity (RAWR). I don't have the Dodge numbers handy, but 3/4 Ton P/Us typically have 2500-3000lbs of payload capacity. Payload being driver, passenger(s), the hitch itself, "stuff" in the cab and bed, and of course the pin weight of the trailer.
A 9000lb dry trailer will probably be 10-11,000 wet. As a guess, assume 20% of the wet weight is on the pin; that's 2000-2200lb on the pin. Depending on the payload rating, that could leave as little as 300lb for everything else in the truck (including the passengers!).
Look at the ratings plate inside the driver's door jamb of your RAM. Find and report back the numbers for GVWR, GCWR, and RAWR (Payload). Then we can calculate a better estimate of your truck's capacity.
By the way, the advertised "tow capacity" is correct only if the moon, sun, stars, and all the planets align just right. Usually it's for a regular cab 2WD standard bed with minimal options and just a single 150lb driver as payload.