Rona's Chihuahua is more of an accessory than a pet. Rona Thorne carried the little dog around with her in much the same way that Paris Hilton and other Hollywood celebrities did. He is only seen in the opening scene of "Movie Star."
The chihuahua has a blue collar with a dangling diamond-shaped tag. This, along with the dog's fawn coloring, seems to draw a resemblance to Scooby Doo, or, perhaps, given the dog's size, Scrappy Doo.
Apparently ISIS allows animals in their offices, either that or they made an exception for the well-known celebrity.