Great start, but...
I think a drag-and-drop colour selection scheme would work better than simply cycling through the colours with clicks. That way, players would be able to see all their options from the start. Getting the computer to play codebreaker (instead of only code-maker) in Mastermind is also a lot of fun: especially for children and people who aren't used to the game, even if the computer doesn't play codebreaker per se, keeping track of the player's guesses and clues and providing intelligent feedback when appropriate (e.g., when the user submits a poor guess) would make the game that much more submerging an experience. This is a great start to a game, but it could be much better with a little more development.