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As far as I can tell, the only public transport option is Desaru Coast's twice-daily free shuttle bus, departing at 10:30 and 21:00 Thursday to Sunday only. These are timed to match the ferries departing from Singapore at 9:30 and 20:00 respectively, but they're not of much use if you use one of the other weekend-only ferries that are not timed to match.
Since Grab or similar rideshare services are not (yet?) available in the area, the only other option is to negotiate with the fairly mercenary cabbies who hang around the terminal. We ended up going via Tg Pengelih instead, but extrapolating from that, you should be able to negotiate a ride to Desaru for 60-80 RM or so.