It will (almost) certainly work in GT6. It's a ps3 release after all.
Not sure why you want to buy a same replacement of a product that broke on you. I wouldn't do it really.
Also, if you are interested in 'next-gen' console gaming (late 2013 and onwards) I'd wait for E3 (next month), so there's info on what peripherals are going to work on each console.