Fiirst dog shoot

Nikon D40
18-55mm
f/5
1/60
400

I was wondering what I could work on in the future to improve these types of photos. I already know that the flash should have been off -- that was my mistake. I appreciate the critique!

If this is the built-in flash then yes, it should have been off. But a off-camera flash or bounced flash from the ceiling might work well for this kind of shot. That would still give you some extra light, but without those hard shadows we see here.
The background is distracting in my opinion. I would try to minimize the background by using a shallow DOF if it was this background, and/or move to a better location where the background is farther away so it can more easily be blurred.
Another option would be using a photo backdrop or even a bed sheet for a less amateur looking background.
Whatever you do, be sure the dog's eyes are in sharp focus. That's key for portraits.

I always try to shot my pets with no flash just so they don't get camera shy.

Those are pretty good. Couple of basic tips: 1) almost everything looks better when shot at eye level; and 2) almost everything looks better shot outside in natural light.

I have to agree with what both Matt and Lava said, also I feel that a little more space is needed around the model. The purple tag is also a bit distracting.
The photograph subject matter is great though.........:)

Cute model. Outdoor background might make for some interesting shots, but could be too distracting for the pup. Consider photoshopping out the eye gunk in left eye of first photo.

Thank you, everyone! You were all so helpful, I appreciate it.

Such a darling little model! (I'm not just saying that because I also have Yorkies). I have to commend you for having him in such sharp focus. It is incredibly hard to photograph animals. I don't think the flash being kept on was such a big mistake, it really brightens up the dog and makes him pop against the couch. I would really like to see him in a plain background, preferably not grey or such a similar color so we can really appreciate the detail you've picked up. Also, I would lighten the shadows just a smidge so we can see his eyes a bit better but that's an easy fix with any photo editing software. Hope this helps:)

Hmm. I would say that to get really good portraits of a pet that you have to approach it like you would a human, where you put the subject (dog in this case) in a studio-like environment w/o distractions. You probably did not have that luxury however.

Along those lines though, I think there are too many things happening here to really isolate the little guy, and as a result, the scene looks a tad ad hoc. The couch seems distracting in general, and the pillows being cut off in both shots hurts too. Also, if you are going to do a crop, it would be good to do one a bit tighter in to avoid the impression of it being a mistake, as it looks in the first shot where the pup's feet are cut off.

I do agree that the lighting's not the best - seems harsh, but I would assume that you don't have studio lighting, so might be all you can do.

The dog does look comfortable shooting w/ you. He might therefore be up for a reshoot :)

G

I agree with the background suggestions. Certainly would like to focus more on your adorable subject.