Wow, very cute and adorable. I like the artstyle and the movement feels nice. Was it a conscious choice to make the platformer stages' background simpler than the overworld? I didn't even notice until seeing your screenshots :P
Will you add a lifebar/allow more hits in later versions? While I love the look of shock the turnip gets when getting hit, I imagine it might be tough to add challenges and keep the game relaxing while only giving us one hit. Oh and I do have to mention that it's rather interesting that to go to a forest stage, you enter a house, but who knows, perhaps that's just how turnips roll.
As for the overworld, will there be some gameplay mechanics added there? Doesn't need to be action, but rather things like solving minor puzzles to continue or farming(this one sorta seems like something you're going for?)
Oh and one bug you might want to look into is that I kept getting fullscreen, despite picking Windowed mode. The resolution did go through, though.
Looking forward to see more of this one :)