It is not cheating to start your project before January 1st. This isn't a competition, so there's no winning, losing, cheating or fair-and-square rules anywhere. If you so desire, you can work on something that's been your primary project for a while and just try to complete something within it; this can be literally ANYTHING, as long as it's code.
As stated, I'm working on an idea from the game I entered last year, only the project and idea has changed so much it could be considered a completely different game (it is, actually, but it's still based off Coins Galore). For all you guys know, I could have been working on it for six months already! But I haven't, I only started the level editor a few weeks ago. And I haven't even built the game yet, so there's still a ways to go.