If your pet is injured or killed by another animal, you may be entitled to receive "compensatory" damages from the owner of the other animal.
The amount (case value) may include the purchase price of a similar pet, registration of a purebred animal, licensing, shots, and training costs. Additionally, if you spent additional money on your pet -- other than for normal veterinary bills -- you should be compensated for such sums. Those expenses have to be reasonable but you can certainly make the claim.  In some cases, you may be able to receive compensation for mental anguish, loss of the companionship of the pet, and even punitive damages.  The claim would be for you, and not for the dog that was injured or killed as California law does not compensate for a lost animal's estate as animals cannot have estates.