The Doctor was a remarkable liar. Death could be three steps from the door and he'd likely still be wearing a smile - at least, if he thought there was any chance that people might panic. He didn't know Hank well and, as a result? He wore his best poker face.
"Alright. So not vicious - just interested in freedom. Not too unreasonable, our beastie." The Doctor tapped a few fingers to his cheek for show. "Right. And possibly confused or startled. Only bites when confronted."
That was a positive bit of information, really. It meant -- "I think we can catch our canine friend. I'd like to meet it."
A normal person would've explained why - that, if the spectacular transformation that Hank had undergone was truly the result of the bite and not some other factor, finding the origin was the best way of gaining information. A normal person might also have reassured, or suggested running some tests.
The Doctor? The Doctor pulled a seven or eight-inch metallic object from his pocket, flipped a switch, and waved the object in Hank's direction. In truth, the sonic screwdriver wasn't likely to tell him the first thing about Hank's prognosis. He was fibbing.
"Stuck? Nooooo. No. Two big brains, we'll reason you out of this."