DPS has airside transits available at the International terminal, though there's not much in the way of service desks there so it might be a hassle if you're on two seperate tickets. I've been through there before when QF used to fly to SIN via DPS (and still do from PER for the time being) and you get hearded through the transit entrance and into the airside departures area of the terminal.

The signage isn't great, but when you arrive in DPS the first time I'm sure you'll spot where you can do an airside transit. Luggage can be interlined through in DPS as well, so long as both carriers support it (was certainly able to interline between Garuda and Qantas in the past for instance).