Anakin was knighted, near as I can tell, somewhere between 4-6 months after AOTC, and it was very much a battlefield promotion - skipping the Trials entirely. It would have been sooner, as the decimated Jedi Order was under pressure after Geonosis to promote all older Padawans to knighthood immediately (according to the first chapter of the book Clone Wars: Wild Space,
set immediately post-AOTC), but Anakin was nowhere near emotionally ready. Most of the pre-2008 Clone Wars EU belongs in this time period. The novel Jedi Trial
tells the story of Anakin's second solo mission, the success of which helps convince the Council he's ready to be knighted (as seen in the microseries). He gets his scar from Asajj a few weeks after that (once he's had a chance to grow his hair out a little), then receives Ahsoka as his apprentice a month after that (7-9 months after AOTC).