You can do this with a single live-action camera (and a good bit of hard work).
You start with a SynthEyes object track: a collection of features on the animal's head are identified and tracked that move rigidly together as a unit. Any features that move independently must be excluded, such as existing mouth or ear motion. The result of the object track is a "null" that it moves and rotates in 3-D, matching the motion of the animal's skull. The background may also be tracked.
The 3-D track is exported from SynthEyes to a 3-D animation system. A new head scan mesh is parented to the null; the head scan then matches the motion of the live-action head exactly. The head mesh can then be animated normally to make the animal talk and show expressions.
The resulting animation is then composited back into the original footage. Depending on the details, additional paint work may be required to restore portions of the background that were originally covered , but that aren't covered in the animated footage.