Hopefully we'll get some responses from some pilates professionals and our Master Trainers, but here is advice we've heard from others with this issue.
This can be a really thorny issue, and it would be really hard to say whether it ethical or unethical with just a little bit of background information. It helps that you are not going to try to solicit or take away any of your current employer's clients. While it may make it a little more difficult to get started, it will hopefully show your current employer that you are being honest in your business practices and may help you maintain some relationships there, especially if you are offering services that they themselves aren't interested in providing.
One really important question though would be whether you signed any sort of non-compete agreement with your current employer. The terms of such agreements can vary, but if you did sign such an agreement you may be restricted from opening a competing business for a certain period of time after ending your employment there.
I'm sure you are trying to keep your costs down but if you're contemplating starting a new business, you may want to contact an attorney anyway and discuss this and other issues you will have to consider, such as liability issues and insurance.
Lastly, take any advice you get here or from anybody with a grain of salt. Each situation is unique, and you should use your best judgment and common sense to keep you on the right track.