I couldn't do much today, but at least I added collisions and jumping. You won't see much difference, but now there's gravity pulling the character down and she's colliding against the floor instead of having a fixed y position.
After jumping or attacking, the character doesn't resume movement if the right arrow is pressed, I will try to fix that tomorrow (Fixed, I should totally go to sleep now). Also, either tomorrow or Friday I should be able to start adding enemies and stuff.
My initial idea was to let the player move freely through the map and have as a level goal clear it of alien enemies. I'm thinking now that an easier option might be make it endless runner style and have a certain amount of time to kill as many enemies as possible. I wish I had time to try out both and see which one is more fun, but I doubt it will be possible.