That doesn't sound stupid at ALL. It's obvious that Izzy is your heart dog. Even after she is gone, she will stay with you in your heart and in all the good memories you made with her. She will never leave you! I bet she loves you just as much as you love her!
We all (I think) feel the same exact way as you and us crazy yorkie ladies get it, even when our friends and family don't
You are a good mommy and I bet Izzy feels special to have you!