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If a dog is only property, then the 'attacking' dog would also be considered property as well, no?

If that's true, worst I can see is a 'destruction of property' charge for actually shooting it. Now the act of unconcealing your weapon may be the stiffer of the charges possibly faced.

Personally, if a dog attacks me or my family (I consider my pets part of my family), I would put it down.
For all I know, the dog is attacking because it has rabies, or was a trained attack dog that is precursor to someone attempting to rob me, or something. (Would trained attack dogs qualify as a 'deadly weapon'? Lethal Force? Possibly.)

I can't see anyone getting charged with shooting a dog that's attacking their dog, or themselves, on their property, or with that person out somewhere, like in a public park.

Now, I'm not talking about a little scuffle between 2 dogs on leashes.. I'm talking about serious bites, bloodshed, an unleashed dog behaving in an obvious threatening manner that cannot be avoided. (turn around, walk away, go around, etc), or a dog clearly fast approaching you with the obvious intent to attack.