I want to put something down on dirt so that my dogs don't kick up so much dust, and don't get so dirty. Is this a good choice?

Yes. It's a great choice, but I would still use a landscape fabric underneath the mulch. It will keep weeds out AND keep the dust down!

I put landscapping fabric down because after about a week the grass started coming through. The one thing you might watch out for is instead of dust, you'll be kicking up bits of rubber mulch if you get to rowdy in the mulch.

These are great for that, my dog loves rolling and running in them. We hit the dirt real good with Preen for weed control but skipped putting fabric down.

Questionable, though dogs eat anything, weeds do grow through add a weed sheeting product.

We've had it down for a year now and are quite happy with the way that it has held up and held its color. Not having dogs, I don't know if they would "go" in it, or continue to use the yard area, but if they did go in the mulch it would be quite a problem to clean up. We put it down over old style mulch, without using plastic or anything under it and did not have weed problems.