It depends on how complicated you want to get with this. The pattern looks like you could do this as one piece, cut the yarn, run the yarn through all the stitches with a tapestry needle, and fasten off. It might be a little bulky but this is the simplest. I have a favorite hat pattern that's a similar two by two rib with decreases at the top. My decreases are: k2tog, p2 tog across the first row. Do two rows of k1, p1. Then two rows of k2tog all across. Maybe this will work for you?
Welsh corgis are cool.