I actually have two coaches that I work with for each class I take. One is usually the intern, but knows how to skate just as well as the coach that works there professionally. I've been thinking about getting a part time job in order to save up for private lessons alongside the adult classes so that I have a coach working with me one-on-one. I don't really know if this is the best course of action though.
That sounds like a sound plan, if you ask me. Getting individualized instruction through private lessons is generally a good way to improve faster.
Though, how much faster depends a lot on a variety of factors: quality of coaching, quality and quantity of practice time outside of lessons, innate talent, physical assets or limitations (such as age, strength, natural flexibility). As many other posters have pointed out, there's no point expending energy comparing yourself to other skaters, especially in things you can't control (such as age, talent). Instead, focus on things you can control (such as seeking out quality coach and practice time, strength and flexibility training).
I reiterate that you should still talk with the skating director, your coach(es), fellow adult skaters, fellow kid skaters, as many people as possible. Ask them whether they focus on tests, competitions, shows or something else. Ask them what system of tests they follow (see also gkelly's highly informative post) and how their coach preps them for it. Ask them how they many lessons a week they think is enough for the rate of progress they want to achieve. Ask questions that are as specific as possible. Everyone will give you a different response, some people's opinions carry more weight than others, but it's for you to assimilate the information and decide the course of action that works best for you.