Oiled cloth is a good idea. (I think "oilcloth" is a different thing altogether, a glossy precursor to plastic - tablecloths were made of it - that's perfectly waterproof but doesn't breathe at all) I have an Australian (Driza-Bone) driver's coat made of oiled cotton that does its job well and has a pleasant smell.

Yes, this is what I was thinking of. Did not think they were two different products. The Aussie coats look awesome. Have been often tempted to buy one but don't really have the need.

Look on Pinterest for a pattern. I found one to make my DGD a Halloween costume. Free

You could practice with the plastic bag shown in the video below then if they don't object too much to a poncho make it from fabric. You could waste a lot of bags getting it right then go onto fabric and use the plastic for the pattern. Post a picture of your pooch in their walking duds.
~http://www.wikihow.com/Make-a-Plastic-Bag-Poncho-for-Your-Dog

Depending on how long you want the poncho you might be able to use the fabric's width as the poncho's length. This would allow you to use the yardage length as the poncho's width. Another idea maybe searching directions for caftans. Wool is warm even when wet. If it's raining cats and dogs you may want a waterproof raincoat instead.

I tried to make myself a poncho using a pattern. I think I would have done better without the
'formal" pattern and just making one I understood!