couple solutions.
My two cents.
1. check out IKEA As-is section, they have tons of cabinet doors of various size, might find one that fits. You might have to refinish to match the stain.
2. Buy some crown molding, cut with a mitre saw, and frame the door, like a picture frame, you will need to do the same for the other drawer doors too. But hey, you might as well give them a face-lift while you are at it. If the doggie chews off another piece, you just replace with a new piece.