A woman traveling alone doesn't really require any different planning than a man traveling alone has. You simply need to use common-sense and you should be fine.

Some random thoughts:

* Yes, you will need seed money to get you started. Either get a less expensive car or wait until your current car is paid off. Remember, you will still need to carry insurance on your car and will need to have some money set aside for potential car maintenance issues, maybe even repairs. If you can, put some money aside specific for that.

* Either find a friend to have your mail sent to, who can forward it onto you at points along the way, or hire a mail forwarding service. I suppose things like auto insurance bills would be your major concern here. Maybe your cellphone bill, if you have one?

* Get a AAA membership or some other roadside assistance program. One tow if your car breaks down more than pays for the membership. And then there are all the free guides and maps that should be useful.

* Place to stay? Why not camp? Much cheaper. Safe. Buy a tarp or free-standing canopy for if it rains.

If you're willing to work any kind of job you can find, temporarily, for seed money to move on down the road, I don't think the lack of RV should be a factor. I have some friends that lost everything they owned in a bankruptcy. Totally broke. Their only seed money was the money they got from garage sales when they sold most of their belongings. They had a mini-van, 4 kids ranging from about age 2-10, and a dog. They kept their tent and camping gear. They sought out free or very low cost campsites on national forest/BLM land. Sometimes staying free for 14 days at a stretch. (After 14 days, you have to move to another campground.) Dad worked at day labor jobs for extra grocery/gas money. And the wife and kids just camped. It gave them time to re-group and consider their options. Decide if they wanted to move and check out towns where they thought there might be opportunities.

Anyway, if they can do it for 3 months with 4 kids without an RV, so can you. While an RV can make things handy, if you can't afford it, you can't afford it. Look for viable alternatives.

Maybe you can sell your car and get an inexpensive van that can be outfitted for sleeping/camping? Or a small pickup with a canopy on it? I met a lady once at a campground who travelled full-time in a much older pickup (I think from the 60's). Not restored but kept in good shape. She had a regular truck canopy on it that she put a piece of plywood on top of the wheel-wells to create a sleeping space. Her gear went below that.

She did something kind of clever. She had extra hooks welded to the top of her camper, spaced apart the same distance as the grommets on tarps. So she could hook a tarp onto the roof of her camper. With the camper backdoor opened (swing-up kind) she could create a space about 6' wide that angled back about 8-9 feet from the back of the truck. Creating a privacy screen and protection from wind/rain. She sat up her chair. Cooked on the tail-gate. Very handy. If I remember right, she had been living this way for about two years or so. She was probably in her early 60's.

Of course, she was probably retired so jobs weren't an issue. Which brings me to my major concern....your dog. What are you going to do with your dog when you're working? If you can afford a weekly/monthly hotel room or short-term apartment, I don't believe many/most will alllow dogs. Even if they do, few will allow you to leave the dog unattended. If you're camping, you can't leave your dog in a campground unattended. And, of course, leaving the dog in your car all day isn't very good for the dog. And can be deadly if it's warm out.

So while I think you might find work via day labor places (usually physical labor jobs like warehousing, cleaning, etc.) and maybe get some work at temp agencies. I'm concerned about what doggy will do when you're at work. What are your plans for him/her?