Not sure if you are willing to travel to NJ but there is this race I ran in May. Over 1100 runners/walkers, at least half of those with dogs! Never seen anything like it.
Check out the second guy overall. He and his dog ran 5:38 pace!!!
I've got a 13 year old running dog and we just ran 10 miles on trail Sunday. It was a big event because it was the first time he's run 10 miles since rupturing his CCL, the canine equivalent of an ACL, having surgery and completing the recovery protocol. When we were younger, he would regularly run 5ks under 21 and complete trail marathons while taunting us humans the last 6 miles. What I have observed is very few race directors will allow dogs to accompany runners when asked in advance but I've never been pulled off a course for bringing my dog to a race. It's easier to ask for forgiveness than permission.
Keep your dog under control at all times and out of the way of other runners and you should have no problems...Jim Pate and Trail Dog Danny