Well, C., my first thoughts were that you are lucky that you are not fighting with your daughter every morning to put her shoes on. My thoughts are that she is very proud of her accomplishments of being able to do so much, and wants to excell. Being first is one way to measure that excellence. So, this may not be totally bad. I would also like to put forth that being conpetitive is very goal oriented. Many young people today have no goals, and do not know how to set and work towards goals. It may be better for her to try to be first than it would be for her to not care about anything. I see that in so many youth today, it becomes a big problem in later life. And, if she wants to achieve that win by her actions that is a BIG plus, many today want to win but want it handed them on a silver platter.
Maybe you could change her focus from just being first to thinking of quality of the experience. Instead of who walks the fastest, maybe make it a game to find as many beautiful things in the world as you walk. Birds, flowers, clouds, all can become their own rewards. Making her feel special when she gets her shoes on quickly may change her from wanting to be first to wanting to be recoginzed for being good at putting on her shoes. Maybe that is what she is looking for, some marker to show that she is good at a task. Give her that positive feedback and see if it works. But, don't discourage all competition, it serves that good purpose of learning how to set and achieve goals.