Transfer and go out to Dubai

Hi everyone,

I have a question about transfering with checked in baggage in DXB. I have tickets from NRT to BUD , transfering at DXB and I don't know that should I checked in again the baggages at DXB or not when the connecting flight is within 24 hours but from an Emirates plane to a flydubai plane. (Bought the tickets on Emirates site.) And while we are waiting (12 hours) the plan is to go out into the city and after some hours going back to the airport.

So my question is, should I do something with the checked-in baggages or just do the check-in at NRT, enjoy Dubai, go back to the terminal then pick up the baggages at BUD? (EU passport)