"IsThis question ("Is time simply the rate of change?" I think this question) is too ambiguous as stated to have any meaningful answer. I can think of interpretations in which the question is vacuous (begging the question: "what is meant by 'rate of change'?"), tautological ("rate of change" == d/dt), or in which the answer is 'no' (GR).
You might find the answer you seek in this book:
- From Eternity to Here: The Quest for the Ultimate Theory of Time by Sean Carroll.