Very nice game! Graphics, music and everything seems consistent with one vision! It gives the player one amazing solid experience.
I think the levels are accurately balanced. Starting with simple levels presenting the controls and mechanics to the player, and later on, getting more difficult. I know it was mentioned in the comments above, but the only thing that kind of threw me off the immersion was the saving system. Starting all over is quite brutal and makes the game more challenging.
I like the idea of not being able to jump with the egg. This mechanics is forcing players to make more strategic moves. Also, giving egg "life points" is a great idea! Overall the game feels very polished. I enjoy playing it! Great job! I will definitely come back to finish the game later!
Btw the browser version doesn't work on safari, I tried opening it a few times before switching to chrome.