Yes you can, and don't call me Shirley!

All you need to do with your DSL connection is to move the Modem, Router and computer to another room that has a phone line in it and plug the modem into the phone outlet.

DSL works by sending the data signal down the same pair of wires as your telephone uses. That means that DSL service is available at any of the phone outlets in your house.

Those filters that the Phone company gave you; they are what separate out the data signal from the voice signal and stop you from hearing high pitch screeching on your line.
Just move, and attach the relevant filter to the next phone outlet.

I'm surprised that the phone company made you purchase a router. Most DSL installations come with a modem which has a router built into it.

P