A 15K trailer will have about a 2800# pin weight which counts against your payload.
Depending on cab configuration, 4 x 2 vs. 4 x 4, rear gear and bed length, the 2008 dually is rated up to 4850# payload (passengers, gear, fuel, tongue or pin weights, etc...), a Gross Combined Vehicle Weight Rating (GCVWR) of up to 24,000# and a max trailer weight of 16,200# depending on the truck's configuration.
The numbers vary depending on how the truck is configured.
Is it a regular cab, a quad cab or a megacab?
Is is 4 x 2 or 4 x 4?
Is it a long bed or a short bed?
Lastly, as you go up in option packages, the truck gets heavier which takes away somewhat from towing capacity. Is it an ST, an SLT or a Laramie?
Here's a link to all the specs on the various configurations of 2008 trucks that may be helpful to you when figuring the weights:
http://www.rambodybuilder.com/2008/docs/dr/mlup3500.pdf
There are some pretty good towing weight calculators online you can use to determine whether or not your truck/trailer/payload weights are under or over the max the truck can handle. The information in the link above will get you started if you want to do the calculations.
I'd say the truck would be able to handle a 15K trailer but I haven't actually weighed it plus the trailer and your truck payload. Of course, you don't want to be over the GCVWR if you get stopped and inspected.
