There are a couple of things that you can do here. Perhaps the simplest is to pass the yarn through one edge to the wrong side (the side that will be on the inside of the finished sweater) and work a conventional seam. Put the two right sides (the sides that will be facing out on the finished sweater) together and seam with a running backstitch
(two stitches forward, one stitch back). You can pin the two sides in place to make it easier to hold the edges in place.
If you do increases or decreases one or two sts in from the edge in the future, it'll make seaming especially mattress stitch seams much easier.
This sweater is really coming along beautifully and will look handsome, I'm sure on your dog. We'd love to see it modeled if you'd care to post a photo.