1. Your dog is your child, his/her needs come before your own, if you can't keep em fed, and hydrated, you shouldn't have him/take him with you. Having said that...Carry an easy portable/collapsible water bowl, not a big ass fuckin jug filled with water already. Look up dog parks along your travels, they almost always have free water fountains for dogs.
2. Be prepared not to be allowed in a lot of places, on buses, and if you're sneaking him on a train hop or somewhere it shouldn't be, make sure he/she knows not to bark and how to remain stealth. Hitching will be harder if you have a scary dog, yes.
3. Why would a cop fuck with you for having a dog? Unless he is somewhere he shouldn't be, or isn't well trained and he fucks with people, and in that case once again he should not be with you.
4. If you're going to have to leave your dog tied outside a store for a short period, make sure he knows to bark and cause commotion if anyone comes up on him. Mine will even guard my shit for me. And keep a damn eye on em, get in, and get out. Don't trust anyone else with your dog, would you let a stranger hold your baby while you went into a store?
5. MAKE SURE YOUR BOND IS A TRUE ONE- if you don't treat your dog with love, you won't get the "obedience" or in my eyes, acting out of love, that you need to ask these things of him/her. If it is a true bond, your dog would do anything for you, not out of fear or expecting treats, but bc they love you, and only want to make you happy.
I kind of think you should travel a bit on your own first so you know what the hell you're doing before you bring another life into it...but that's my personal opinion...
Hope that helps you. Peace.