Oh that is just so sad that Tia is not doing well. Its the worst thing to go through, isn't it....the fear of the time when we lose them. I'm so sorry you're having to think about that now.
It might be hectic on the one hand to get this pup but on the other hand, it would probably make it easier on Tink to have had a chance to bond with the new pup when the time comes to say, "good-bye" to Tia. That won't replace Tia, but it might take the edge off.
Poor Tia...I hope she will feel better and have some more good time with you. My heart goes out to you at this time when you're all churned up and not knowing quite what to do and you have this poor little gal who is not well. I wish there was something I could do or say to help.
(((hugs)))