As seen on MC1.7.10 with Doggy Talents - v1.9.0f
When invulnerability is enabled, killing the dog still gives drops and bonus while it remains alive.
For example with Magical crops, you can get infinite minicio essence, same with Grimoire of gaias shards and fragments, Witchery wolf tongue and head.

Yes I am aware of this problem with some mods and was going to look into it soon