My whole entire life I thought it was, for example : Timmy and I, but as I learned more about it and how English has been changing it is now : Timmy and me. Me is an indirect object because me isn't the main focus. Your answer is me; indirect object.
Will you call Katie and me when you’re ready to leave?
To check just remove Katie from the sentence.
Will you call I/me when you're ready to leave?
Me makes more sense then I.
Hoped I helped!
(Btw : You is the subject because that is what the subject should do)