A woman tried to book a stay with me, and asked me to drive to another state to pick up her dog. Is this normal?

A woman tried to book a stay with me and asked me to drive to another state to pick up her dog. She said that her dog is not being treated well in the original pet care location and would like for me to go and get her. I'm not sure if this is a scam or for real, and it takes several calls to get a hold of this woman. When she does answer she tells me she's leaving the country and will have to call me in a few hours to give me the details of where her dog is currently staying. She tells me that she found the sitter on another site and does not know her details, which makes no sense. I feel as though I should tell her I cannot take her dog, but I do not want to be the reason her dog ends up staying in a bad situation. This whole situation is extraordinarily sketchy.