Dog scabies is a different infection commonly known as mange. The species of mite that infects dogs is different than humans. You can get a rash but it will tend to be very localized and will go away on its own. You can't get the horrible spreading infection that can be really hard to get rid of unless you get the human version, and the same applies to human scabies and dogs. They're not interchangeable. There are a series of steps you need to take with scabies to make sure you thoroughly killed all the mites and their eggs so you don't get reinfected. For instance, they tend to be in bedding so if you put used bedding aside and away from human contact for a week, maybe even two, all the mites will starve to death. Then you can just wash it and it's safe to use again. You can try certain harsh cleaning methods, but to be effective, they might be hard on the bedding too so it's best if you can just not use it for a while.
They subscribe a poisonous lotion that you have to cover every inch of your body with from the neck down. You need to be sure and get it under your fingernails. The mites love to hang out there. They often get there when you scratch. Missing spots is a way the infection can come back later. It's takes 2 to 4 weeks for symptoms to show after infection so you can be infected and not know it. Also, you can feel relief and not realize you missed a few mites and then the rash can come back. Alternatively, you can kill all the mites and still be itchy for quite a while afterward and think you're still infected when you're not. You just have some lingering dead ones making you itch until you've sloughed off a couple layers of skin. All you can do is be really thorough, and that's usually sufficient, and then wait a while before you can know for sure that you got rid of them.
The rash is basically an allergic reaction to a mites bite and its body or eggs, dead or alive. Any antihistamine, local or even oral, will help a lot with the itching until you've gotten it under control.
http://www.webmd.com/skin-problems-and-treatments/tc/scabies-topic-overview