Dragonborn will be the first to touch down on the PSN on February 12. Hearthfire will follow the week after on the 19 and Dawnguard the 26. Each DLC will be on sale for half off the week that it's released.
Unfortunately, these release dates are North America only. European release dates have yet to be announced.
Skyrim DLC has never made it to the PS3 in the past due to technical issues. When Skyrim was first released, PS3 fans were forced to suffer through a save glitch in which the game would be rendered unplayable once save game files exceeded the 5 MB size.
All DLC has already been released on the Xbox 360. Dragonborn will be coming to PC gamers Feb. 5th.