Convincing parents to get a new dog after the death of ours?

We recently had to put our old dog to sleep after 11 happy years. My siblings and I all agreed that we want to get another dog. But my mom refuses to even hear it and says that we will never get another dog. So I wondering how I can convince her to get another dog. She says she will feel guilty or like a traitor if another dog comes into our house. Thank you