The filling should be bubbling around the edges and the topping should be puffed and browned.  For the most accurate way of testing, insert an instant-read thermometer into the middle of the cobbler. It should read 200 degrees.
It's OK if the filling is a bit runny, as that's the nature of a cobbler. But for a thicker filling, watch for some bubbling in the center of the cobbler as well.