The answer to this question largely depends on whether the game has been designed as of yet, and how complex this game is. There are competitions in which teams of 3 or 4 people complete a game (design, graphics, sound, game-play and all) in the space of a (sleepless) weekend. They aren't generally very complex at that point, but they are by all means a complete game.
On the other hand, the people participating in these competitions are largely people who know what they're doing. They have someone dedicated to sound, someone dedicated to graphics, and at least one person dedicated to programming. If you have little idea what you're doing with any of those (either through lack of design or lack of experience), then that adds time, and that time could be significant.
Given this background, I believe your will be possible in two months, and you will not need to be full time to accomplish it, though you may need to dedicate a majority of your time to the project. There are several reasons for this:
- Educational games are generally fairly simple
- Games for that age bracket are generally fairly simple
- A high level of graphics seems un-necessary
- Educational games have a specific goal, and thus are less susceptible to over-design
- You have experience with HTML5
Now, that last point could be valid, or it could not. If, for instance, you're required to use <canvas>, and you haven't before, you could be in trouble.
Otherwise, with the information given, and under the assumption that some direction is given as to the design of the game, I think you're in good shape.
Good luck!