Hello D.: How wonderful your daughter is taking the lead. Now is a perfect time for you and she to understand your different roles to set-up an expectation for the rest of her & your life. You say she is "strong-willed." If you help her understand that she can make great decisions for herself now' then, that is more likely to run it's course as the teen's come (which can be the toughest for especially parents) - help her understand that she is making a great decision to get out of diaper's and start becoming a "big girl" and how we grow - little, by little and she will be making decisions for the rest of her life one decision at a time (so not to overwhelm her)and make sure you do 3 things:
1. Tell her how proud you are of her (with a great big smile and lot's of hugs -whether she succeeds/fails).
2. Guide her in the direction "you" want her to go. Example: "Do you feel like potty(/whatever word you use)?" or "Would you like to wear underwear or diapers/pull-up's today?"
3. Above all - Be Patient. I can't express that enough. Patience - even though she may be strong-willed, highly intelligent etc... She is still only 2 and will be little for a long time.
Just to let you know - incase: Many time's when children potty train - they may have a short-regression period - peeing in bed etc... No worries... Just put pull-up's back on and let her know "it's okay" she will succeed because that is who she is - a success.
Hope this helps. I am sorry couldn't get into it more. I am sharing my computer with my hubby for now. A little about myself. I am a mom of 2 boy's, 17yrs.(couldn't wait to be a big boy), & 4yrs (hates the thought of being a "big boy"(both strong-willed to the max. & highly intelligent kids (both completlty different)- I mean the kind of kids that make a parent feel "stupid" - and I decided to at least be a good challenge for them to help make a win-win situation. After all I am the older one and have more experiences, that, makes me wiser, plus I read a whole lotta books/seminars/classes etc....
I am married and am grateful I have a wonderful family to lead.
Best of blessing's to you and great job on understanding your daughter at such a young age.