Well hmm...i dont know if there is a direct route to QR, but there is a train that goes to ipswitch and futher i think, havent done it personally.
As for cheap motels...the futher you get from the coast the cheaper it gets. So myabe nerang..which is 5 mins inland, is prob a bit cheaper. and there is a train station in nerang. might be cheaper hiring a car for the day and driving buddy, and more convenient.