It sounds like you’re a teacher of some sort, so not only is this very do-able for you, it’s actually quite common. In fact, the day that I completed the AT, alongside me on Mt. Katahdin was a teacher who had been section hiking it (in 100-200 mile increments) every summer over the course of 18 years. It was an amazing experience to witness and be present to someone with that much drive & desire finally accomplishing their goal.
To your point about being a female and feeling vulnerable, I’ll tell you that the thru-hiking community / subculture that exists (particularly on the AT & PCT) is unlike anything that you have ever experienced and (assuming that you have some basic common sense) you have less to worry about on the trail than you ever would in your everyday life / wherever you might live…… I know and have met 100’s of single (solo) women who have hiked without incident as once you settle into a groove with other hikers, you will (literally) have 20 big brothers, several over protective fathers, a couple surrogate mothers and a sister or two constantly looking out for you. It’s the type of culture that will restore your faith in humanity (if yours has ever waned) and it’s one I long for in my everyday life, but alas here I am.
Taking a dog along: Please, don’t do it! It can be done / don’t get me wrong, but unless you have a degree in Animal Science, a lot of experience, and the discipline of a Zen Buddhist master, it almost always ends in disaster for the dog. I’ve seen far more (at least 50/1) miserable dogs than happy ones on the trail and it breaks my heart when people put their own needs first at the cost of a dogs soul (and the pads on their feet) just because their ‘person’ desires a companion………