I lean towards the idea that you should get the degree. This is why.
It's wonderful that you seem to know what you want to do, and I agree that you should pursue it.
However, sometimes our plans or preferences change. A profession that may have interested us at one time in our lives may, for various reasons, interest us less, become unavailable, etc. So it can be important, especially earlier in your life, to have backup plans.
A good way of thinking about this is PACE. Primary, alternate, contingency, emergency. Cosmetician is your primary plan. And that's awesome. But suppose one day you find that it's not what you thought? That it's not enough? That you decide you really want to teach? That the income/uncertainty isn't sufficient for your family? etc.
So what's the alternate? Let's say teaching. You'll need a degree. As you go forward in life, your responsibilities will accumulate. You may have familial responsibilities, debt associated with a home, and so forth. It becomes increasingly difficult to go back to school.
At this point in your life, though, it's much easier. You are already in a degree program, and are only a year away. Finishing the degree will give you a better ground should you at some point decide on an alternate plan to being a cosmetician, and will make that plan much easier to carry forward.
Finally, remember that employers will look at whether you have a degree beyond high school. It's a mark that you were able to complete the program, that you're reasonably intelligent, and that you can handle responsibility. So having the degree on your resume, particularly if you finish with a good GPA, will aid you in ANY career. Further, if you lack any degree beyond high school, it will signal to any employer that you don't have many other options, which will reduce your bargaining power and perhaps lower your earnings over your lifetime.
My advice therefore is to finish the degree now, while the cost of doing so is lowest and you are most able to do so. A year is a fairly short period of time. In that year, crush your remaining classes. Put your heart into it, get the best grades you can, and then become a cosmetician. The degree, even if it is in a subject unrelated, is an achievement nonetheless that will aid you in any career, and will become especially important if you decide to change careers, as many people do.