It's good that your DD is noticing her personal hygiene and wearing deodorant for sport when she would be getting more sweaty. That or she could just be copying what you are doing, or if she has seen peers doing it. Either way, I don't think it's a definite sign of puberty, unless she has also started growing underarm hair, pubic hair, breast buds etc
As a note - spray on deodorant is banned from schools because of the potential for it to trigger asthma attacks in other students. Most people think this ridiculous, but it is important to consider especially once they get to high school and you have 30+ students putting deodorant on in a change room after sport class.