I'm very sorry to hear about Toto. I know that your heart will lead you to the right decision about what to do.
As far as your friend goes, I would feel the same way. It's not fair to you to pay for more than your fair share. It sounds like she may be hestitant about getting this dog...so I hope that if she does take it, she is ready for the responsiblity.
I would just suggest being honest with her. Just tell her that if she is committed to getting one of the dogs, that you are not comfortable paying for more than half and that you hope she understands. Hopefully, she will.
Also, do you know why she only wants to pay $125? If its not financial, I wonder if she has another reason. If that is the case, maybe you can talk it over and address her underlying concern.
Good luck!