I think you could just work back and forth across the chest part and leave the top stitches on the needle. Do a gradual increase from the center of the chest. Kind of like work to 10 stitches past the center of the chest, wrap and turn, work 20 stitches, w & t, work 30 st, w&t, work 40, w & t, etc, until you have the chest the depth you want.
Now, mind you, this is just off the top of my head. I haven't done it, but this is what I would try.
If you think it would work better for the shape of your (adorable) dog, maybe it would work better to start the short rows wide and gradually make them narrower. This way you could pick up the wraps from the previous rows.
Either way, when the chest part was deep enough, you could just knit a round or two using all the stitches and then rib for the collar.
I hope this makes some sort of sense.:lol: