I agree. There is no moral problem.
You were working for her. She benefited from the fact that you were there. She wasn't doing you a favor "teaching you everything you know". What she taught you, she did for her benefit, not yours.
You owe her nothing.
You have every right to open up your own store. You can compete with her. You can put her out of business if you want (not that this should be your goal). None of this would reflect poorly on your character-- business is business.
Opening a business is difficult. If you are going to do this, you have to focus on what it will take to make it successful. This other woman is not your concern... let her worry about her own business.
Make it happen.