Lion Brand's links haven't been working lately; at least for me, they direct me to a generic page on their site. Is the doggie sweater you're talking about the "Fun Fur" doggie sweater?
Wow, your doggie must be tiny! Sounds cute!
I don't know what pattern you're using, but you could try just making a tube in ribbing, from the neck to the back. Maybe increase in the chest area, and just leave two openings for the legs to pop through. You could later pick up stitches along the openings if you want to cover the legs, too. So, knit the tube until it reaches the back legs, and then bind-off the bottom and continue on the top a little longer to cover the back end. Round it out like shaping the top of a sleeve, in a curve.
If making your own pattern like this sounds too daunting, maybe someone can point you to a tiny dog sweater pattern! Yellowness was talking about making a sweater for a chiwawa (sp?), so you could ask her!
Hope that helps!