Could use some work in the UX part of the game. It's unclear whether the egg is actually an egg or is your pet, which makes the buttons feel like 'they don't work'. Probably best to grey the buttons you can't use out, show the progress/time until the pet is hatched through cracks in the egg, a progress bar, making the bounce faster or slower, etc, and then go from there. I'd also make the 'hatching' more of a gameplay element than a timer. Get them to tap it to help the egg open, keep it warm, wash it, et cetera; all of that will feel better and won't leave the player thinking 'is the game actually running'.
Could be a good relaxing game, just needs more feedback from the game to the user and a little more polish. Pretty good for just two days' work!