First off, you are on the right path-making it a batlle will only give her negative feelings about toothbrushing. Well, welcome to the wonderful world of motherhood. What I mean by that is before I became a SAHM (after the birth of my second child) I was a dental hygienist for 8 years. So I thought this part should be easy for me, but, ha! it was and still is a struggle. I became so much more compassionate to my patients after becoming a mom.
Eventually I made up a silly song and that helped my son, as did him getting older. I also let him do it by himself when I was finished almost as a reward, plus their effort (as little as it may be) can only help and not do any harm. My son is now 3 1/2 but for my daughter who just turned one, I find it easier to use a wet wahscloth instead of a toothbrush. Also, keep in mind that most children do not build up a great deal of plaque at this age so one really thorough brushing per day should be sufficient. What you also want to keep in mind is frequency of snacking on carb foods (especially sticky ones) and constantly sipping on juice and milk.
As she gets older, you can educate her in simple terms of why we need to clean our teeth and eventually a trip to the dentist should also help. Good luck-hope this helps!