Many of the yarns that Rainbow Gallery has are great for the fur on animals, hair and beards. Generally, they appear to be too large for the canvas. What you can do is use a slightly larger needle that will push the canvas threads apart and let the yarn pass easily through the canvas. When you are going for a fuzzy appearance any distortion to the canvas will not show and will be covered by the yarn. Long stitches will show the effect much better than short stitches. In addition, a split stitch is wonderful to bring the furry effect out, but come up through the canvas rather than down into it.
A needle punch is also a great way to cover large areas in a short period of time. The punch needle will take most of the drudgery out of Turkey Work. Several different sizes of needles are available to fit different sizes of canvas and to accommodate different yarns. Please note that if you use the punch needle to do Turkey Work you will need to glue down the yarn on the back of the canvas. Tacky glue or any fabric glue will work.
Another good tool is a nap brush (Bunka brush). It fits over your index finger and has strong wire teeth that you scrape over the yarn to enhance its furry effect. This technique will lift the fiber from the canvas and make yarn look like fur or hair.