There is a difference between consciousness and sel-consciousness. It is one thing to be aware of things around oneself, or even of one's own physical states, and another to be aware that one is so aware. The latter is self-consciousness. Personality is yet a third thing. As a reasonable first pass we could take it to be a bundle of behavioural, affective and cognitive dispositions. Those would seem to require consciousness, but not self-consciousness.

I agree that this is a hard one, harder of course for you than it is for us, and harder for us than it is for your dog. The last is an important point. Euthanising your dog in this situation will cause you a great deal of suffering, but will not cause the dog suffering. It will deprive her of future pleasure of course, but she will not suffer from knowing that. I think that condemning her to spending her last few weeks without you in a cage would be cruel, and recommend against that course of action. Of course, if you can, you might arrange a private adoption. But if you can't, I think that euthanasia is the most humane option. You can ease your own feelings of guilt by remembering that. But you probably can't do much about the reasonable grief.