How long can I run a vent duct for a new bathroom exhaust on an old house that doesn't vent out properly?
The Panasonic product you listed supports 4" or 6" round duct, according to the installation manual. 13 feet should not be too far at all, especially if it is a relatively straight run. And to be extra safe, use 6" round duct. The rigid kind, not the cheap flex stuff! The increased size will allow less restricted airflow.

Also, try to avoid using any 90 degree turns. The model you referenced has a side port, which means if you install it between joists you should be able to take the duct straight out of the side of the fan and straight through the exterior wall to the vent cap. 

In reality, you should be fine with a straight run of 4" rigid duct. But 6" would give you some peace of mind.