I am to travel SYD-SIN-DME (ret.), but have the sectors in two separate bookings.

Booking 1: SYD-SIN-HKG-SIN-SYD
Booking 2: SIN-DME-SIN

The entire routing will then follow, SYD-SIN-DME-SIN-HKG-SIN-SYD.

I am just concerned that when departing SYD and departing DME, will there be issues with baggage check, since the booking from the port I depart will not include the next sector? Does this prop up any other issues or is this completely common? Thanks.