I enjoyed this. I was frustrated with how easily I died and kept going back to the beginning until I found the door and then it made sense. I like how the gnome fits the tiny world theme and how he has a tiny axe.
Some things it could have benefited from are bigger swing animations and some coyote frames. Extending the swipe from the axe would make it easier to understand where exactly the hitbox extends to; it's also hard to tell how far the hitbox goes in the y direction. Coyote frames would help more with the feel of the platforming. Especially in that section with about six spike pits, it felt like I definitely did hit jump before I fell (even though I know I probably didn't), it would have felt a lot better to play if it had maybe 3 frames after leaving the platform where jump is still available.
I think you did a good job with the time you had.