Sicily - How is my itinerary without a car? too ambitious?

My plan:

Arrive at Catania (2 nights) -> Taormina (2 nights) -> Siracusa (3 nights) -> Noto (2 nights) -> Ragusa (2 nights) -> Palermo ( 3 nights) -> fly out.

It looks like trainline offers trains every morning for it, I dont see an issue?

If its too hard, I can do east side and do this instead too:

Catania-> Taormina -> Siracusa -> Ragusa  -> depart Catania