Find a retreat location and learn an off-the-beaten-path route to reach it. Said location should be close to water, have some kind of stable shelter (you'd be amazed by the difference a lean-to shelter will provide when compared to the open elements.) also camoflouge this area and set up signs that indicate biological or nuclear contamination of the area to deter any intruders, this should keep the distance necessary that your dog wouldn't sound off and blow cover. Other than making it to a decently established retreat area the rest is survival know how. Things like water purification, trapping hunting, scavenging, ect are the real tricks to survival.
If I were you (secretly I am you, I'm 23 from the Appalachian area of VA and a prepper with the foreseeable lone wolf future I assume you're preparing for) I would place food water and weapon storage in this location. Buy havaheart traps to set around this local so if you catch breedable animals you have said option, also ,further out, set snares on animal paths for catching larger game (here's where a gun comes into play, if its your first time killing than a knife will be too personal/dangerous) other deterants of unwanted guest such as marauders and such requires a much more taboo know how but if you're interested in this info I can forward them to you via pdf.
Henry .22 survival rifle (it breaks down to nothing so it's not like having a gun strapped to your back at all times) and a small compact .38 or 9mm mostly used for escaping the suburbs and a just in case scenario.
Be sure your pup makes it with you, companionship (for most people) is essential.
Bandana and charcoal (aside from bleach and potable agua) is the best form of water purification.
Take seeds with you so hopefully you can procure a small garden.
There's literally a 10000000 different things in the guide to survival, pick things you think you'll be good at, gardening, trapping, breeding rabbits and live the best way you can
Good luck and if you want any more tips let me know.