Yep! I had one of those, she is now 9 years old and swims well. In fact, when she was 2 and in group swim lessons, the instructor turned her back to assist a student and my daughter jumped in. Thankfully, the instructor had keen ears, turned around, and plucked her from the water. I kept her in swim lessons from then on. I figured that was the best safety measure I could take with her; teaching her to swim.
My suggestion is to have private swim lessons for her. The instructor will have full attention on your child. Additionally, instructors do not have the same link/fear with the child, like parents do. In that same vein, the instructors goal is to teach water safety and swim skills, so your child is in good hands. Your daughter will be able to excell to her full potential.
I have found the instructors at my local YMCA to be very competent and kind. Plus, most Y's have an indoor pool, making year round swim lessons a possibility.
Keep on Swimin',
M. P