Maybe it's not for fur, but for a more realistic drawing in generals I has a few suggestions.
Shading helps a lot. I suck at shading, since I just draw it wherever, but it really helps.
(Best example I could find since I hardly do shading xD)
I usually don't do shading, but some times I make sure to make the front and back legs that are facing the other way a bit darker, since the front and back legs in front are facing the light source. You can see that in there.
You can also tell that there's no light coming from behind her and that the light source is in front. I am kinda just explaining what I do so maybe listen to someone who knows more than me xD
But yeah, shading helps make it seem more realistic, like they're in an actual place. Just another thing, her eye is kinda glowing in the darker part, imayhavejustaddedthatwhiledrawingthissinceicouldn'tthinkofanything
Also, my favorite part of drawing anything, dem eyes
I use a lot of different methods for drawing my eyes, depends on what I like and how lazy I am
This is the one I've been using recently. I have the iris a certain color, blue here, then I select that with a select tool in GIMP and fill the bottom with a darker blue, then the top with a lighter blue, and sometimes I'll carefully use the smudge tool to make them a bit more... pointy I guess xD
Next one is the one I use when I'm not lazy
I fill the eye up with a certain color, green/yellow here. I select the iris and make my background color a darker shade of green/yellow (can't tell what it is xD) while keeping the foreground color the same color as the iris is now. Then I use da.. blend (had to search for a while) tool, angle it a certain way, then let go, and yay~ Now it changes colors smoothly! c:
This one I used to use a lot but not as often now. I just change the size of my brush to as low as possible, change the color to either a lighter or darker color than the iris, then I just draw mountains almost near the pupil or whatever it's called i don't know things but it makes it look pretty good
Also, I'm not sure if you do or not, but I almost always use base lines.
I can't find an example but they're very single yet help a lot to get stuff right and make sure that the character's posture won't look weird or anything.
That's about all I have, it's early in the morning so this might be a bit confusing

Hope this helps!