Cebu Pacific is a low cost airline, so carry on is included but you’ll need to pay if you want to check a bag. But this is the Philippines, it’s nice and warm!
Personally I’d recommend using Manila as a stopover before flying to Palawan, I loved El Nido especially (fly to Puerto Princesa, take a shuttle).
Dates vary but there are ones almost every month from now until winter next year. I’ve linked to FlightScout as it highlights several of these, but once you click through to skyscanner/trip you can search your own more specific dates.
Airline: Cebu Pacific
Destination: Manila, Philippines
From: MEL/SYD
Dates: various over next 8 months
Flights to Manila from Melbourne
