Fedora 19 will be one of the first desktop Linux distributions shipping with accelerated Radeon HD 7000 series graphics support.
Jerome Glisse of Red Hat has been readying the open-source stack for the Radeon HD 7000 series on Fedora 19. The Radeon HD 7000 series open-source driver support with acceleration requires building the "RadeonSI" Gallium3D driver inside Mesa 9.1/master, the latest libdrm, new xf86-video-ati, the GLAMOR library, and also the yet-to-be-released version of LLVM for its Radeon GPU back-end, beyond needing a modern Linux kernel too.
Namely due to the new Gallium3D driver, the experimental LLVM back-end, and needing the GLAMOR library for 2D acceleration support, Radeon HD 7000 series adoption hasn't been quick. The open-source driver stack has been slow to mature but is now finally handling basic OpenGL in a decent manner while not yet being up to the same level as the R600g driver for Radeon HD 2000/3000/4000/5000/6000 series graphics cards.
The package review request for RadeonSI Fedora 19 support can be found on the Fedora devel list