First off, I really like it & think the variation in stitches won't even be noticeable once it's in a quilt. I had the same problem when I was first learning to applique. Instead of starting my stitching right away, I marked a 1/8" stitch "line" (dots) to follow for 2-3 appliques until I had stitch length down. I took the tip of my triangle ruler to use as a guide; it's 1/4", so I used half the depth. You may need to shorten the stitches as you approach the point, but the stitch line still helps as a guideline. Start to shorten stitches and, if needed, narrow spacing about 2-3 stitches before point or tip of curve on either side -- you did it perfectly with cat's ear.
It looks like your stitches by the tail are and the base of the cat are considerably longer than the rest of your stitches, they are also slightly farther apart (which is actually what you want with a longer stitch -- just usually not combined with the shorter stitches in the same applique piece). Alternatively, you could try practicing on applique that doesn't have narrow parts & do a couple pieces with a 1/4" long stitch, then once you've mastered that work your way down to the 1/8" stitches. Here's a good video that shows some techniques. Use the same technique used on the leaf for narrow curves.
https://www.youtube.com/watch?v=BNK6ebZMxkM
Just as a note: it's not so much the sharp curves that will cause your stitch length/spacing to vary so much, it is when an applique piece gets considerably narrower or wider. The eye is trying to use landmarks to figure out how deep to make the stitches & it gets confused when you start getting narrower or wider with your piece.
Good luck with the applique! I think it is the most fun part of making quilts & hope you come to enjoy it as much as I do!
