Interesting question. Most gis applications to inundation are focused downstream in the event if a dam breach whereas you are looking at upstream impoundment.
Off hand, at least two factors would need to be considered: stream in flow and height of the beaver dam. You'd then need to calculate the volume of the ''reservoir' while considering the surface area and where the low spot is in your terrain relative to the height of the dam. (There may be other parameters to examine as well.)
Just remember that the structural integrity of the structure is only known by the engineer/builder and they won't share that information with you! In other words, a failure could occur way before much water has been impounded.
That should just about do it....