Reading, renting, and visiting RV shows will give you lots of information, but you need a basis for actually processing it, so my favorite suggestion above is to visit a campground and talk to people who seem like they might be undertaking an adventure like yours.
You can't live in a house full time one day, and then start living in an RV full time the next. You need transition time in which you own both and take short trips so you know whether it's a good fit, what vehicle and equipment suit you, etc. A woman traveling alone needs a reliable vehicle: don't scrimp.
The link above with lots of blogs is very entertaining but leaves out my very favorite, which got me started on my own RV adventures. Andy doesn't post much any more, but his story is so detailed and personalized, it gives a good feel for the experience of transitioning to full time.
Travels with AndyTraveling with a pet puts major constraints on you, especially with a dog: How long you can leave the vehicle unattended, where you can park (especially on hot days and some campgrounds don't allow dogs), etc.
There are several reliable mail-forwarding services, you can just pick one. Likewise, handling all your finances (banking, charge accounts, etc.) online is easy and most of those accounts want you to "go paperless" anyway.