The problem with the 9x9 board is that it is just too small to allow you to really play go, it turns into a different kind of game. I think it is better to switch to a bigger board. It doesn't have to be the complete board, you can have some intermediate steps. The 9x9 board can be used to teach the absolute basics, but don't stay on it too long, you are probably not training yourself the right way. If your goal is to beat the computer on a 9x9 that's fine, but at some point it doesn't help you in playing the real game. My feeling is that point is reached real fast.
This is definitely true — 9×9 is too small for a real game. But 13×13 is a much better compromise and I would recommend that to players who have outgrown the 9×9 but still don't need to sit through a two-hour game before they learn from each mistake.
(To be precise, the problem with 9×9 is that often after just a few moves the board is divided into a white half and a black half, and the rest of the game is a yose to decide whose half is larger. I'm sure someone can counterargue that if played expertly, 9×9 is a fascinating and highly skilled game; but in general it's going to lack a lot of the situations you can encounter in a full game of Go.)
