Since you don't even have the dog yet, I'd advise doing the trip and then getting a dog after. A dog will be a hassle on a trip of that nature. You don't need it for protection. For company make it a point to meet the local folks. You will be likely to find tons of chances to chat with them. Also if you camp in hiker biker sites, city parks, and churches you will probably be able to camp with other cyclists if you want.
That said as far as walking the TA... I don't know of anyone, but we met a guy who ran a shorter route across the US. He was on the TA part of the way but his route was maybe 1200 miles shorter. His site is at: http://www.suneson.se/index.php
Check out his Oregon to Virginia trip.
I also would advise that you will not need to stealth camp most of the time. Why stealth camp in places where you are welcome to camp in plain sight? It is a personal choice, but when bike touring I prefer to camp in city parks or sleep in churches rather than hiding in the woods. You get to meet more people that way, and the extra human contact is nice. I think we paid to camp less than half the time on the TA and never needed to stealth camp or knock on doors to get permission. On the TA the trails have been blazed in that respect. Places that will let you camp are mostly known. Churches that will let you sleep there are known, etc. Some places will feed you either breakfast of dinner. It is a nice experience.
Where there aren't free places to stay there are often cheap camp sites for cyclists.