Let me start with a disclaimer - I am not a lawyer and cannot give legal advice. What I am saying is my opinion and my opinion alone. You should seek legal advice from an attorney to get defensible advice.
I am often asked about the use of deadly force to defend a family pet. This is a very tough situation, especially for those that consider their beloved pet a member of the family, as most of us do.
My answer has been a consistent probably not. If the deadly force is employed in a manner that eliminates a threat to a person, then it is a clear no. Sorry...
If the use of deadly force is employed when the threat to the pet is also a threat to a human, then it is probably defensible.
This subject was addressed in a presentation by The Law of Self Defense. they have regular presentations and post them on several platforms.
The specific presentation was discussing an Arizona case of a suspect threatening a K-9 that was assisting LEO action to apprehend the suspect. The subject was engaged by a SWAT officer and subsequently perished.
The question being addressed was weather this was a good shoot. The teaser for the presentation indicated the answer was a no. Their determination (they are lawyers) is that pets are property. In 49 states the only legal force against a human in defense of property is non-deadly. This includes a K-9 in performance of law enforcement duties.
In Texas, however, one would be ill advised to mess with a man’s truck or his dog.
If you want to see their presentation it is available on YoutTube. https://www.youtube.com/watch?v=26HAo9X-OtU
As always get legal advice from an attorney in your area for the best answer.