What is the gauge/weight on the package of the acrylic yarn you were using?
What is the gauge/weight on the package of the wool ease yarn? Sounds thinner.
What is the gauge given in the pattern you are reading?
Based on what you have written, in order to get gauge you would have to keep going up a needle size, but eventually the knitting will be very loose/lacy. I'm not sure you will want this in a dog sweater, as it won't be very warm.