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ioki, as davem stated, there are two secure car parking facilities on the Arterial Road, just past the corner of Nudgee Road. They use a mini-bus to shuttle pax between terminals and their facility. Never used it, but one would suspect that it has pitched it's prices below that of the long term facility.
Valet Parking - a subject icemann correctly pointed out hasn't been broached here - either for a very long time or at all (without having done a search).
I used to use it alot in BNE when going on overnighters or same-day trips(back when I used to live further away from the airport and didn't have a willing chauffeur to come and pick me up :wink: ). Back then it was a little cheaper. Still, for the convenience factor, it used to be great to drive past everybody waiting at the taxi rank...