Update: I have drawn a cat and figured out how it might climb a tree. At first it was just going to be moved around and jumped with the arrow keys, but then I decided I would rather use the mouse. The result is something like this:
You can pick up and move each paw, and the cat goes to the middle point of all the paws. A lot of stuff I thought would take ages, like making the legs work and making the cat go into the middle, turned out to be really easy. And the stuff I thought would be easy was hard. It took me a long time to figure out how to make the paws point away from the cat no matter where you move them to. Apparently it has something to do with trigonometry.
Next I need to make a background, and decide how a narrative might work, and how much of one there might be.
Also, I'm not sure whether to make the screen scroll up automatically, meaning you have to be quick to keep the cat from falling off the bottom of the screen, or whether to make the screen scroll up with the cat, making it more of a relaxed sort of experience. Also I need to figure out how to do either of these things.