The answer to the question posed by the title comes in two forms.
The short form is Yes. There is nothing about being a woman that limits your ability to paint your own home.
The long answer is It Depends. What does it depend on? A lot of factors.
Time is one concern. A single woman has a career to handle. They might even have a child to take care of. When are they going to find the time in the day to paint even a single room in their own home? The logistics of it is a challenge, no matter the gender.
What time of year is it? You’ll want to paint the outdoor areas in the summer because there’s more daylight and it’s easier to dry. Indoors you can do other times of the year, as long as you can get the right ventilation and can clear the space.
Another factor in this equation is cost. Depending on your income, you might not be able to afford to take time off and paint things yourself. Or you might not be able to afford professionals and have no choice but to handle things personally.
If you have friends that can muster up the free time with you, DIY house painting can be a fun way to bond or spend time. Just be sure not to waste time too much and get the painting done.
Of course, this is all moot if you don’t know how to paint. Man or woman, if you don’t know how to paint and the nuances of applying coats, you probably have no business with DIY house painting. You’re more likely to ruin it than you are to get it right.
Long story short, a single woman can DIY her house painting. Any healthy human can. However, if you can afford it and you don’t have the time to handle it yourself, we recommend getting professionals like on the job.