Is it possible for me to get into competitive colleges such as Duke and Georgetown?

I currently maintain a 4.0 GPA, have participated in many volunteer programs, and have well rounded hobbies like horse back riding and swimming. I have scored pretty high on my PSAT, but still have not taken the SAT yet. However, my school does not offer any advanced placement or honors courses! Will that hurt in my application to prestigious colleges, like Duke? Should i be taking online AP cles to better my chances of making it into a good college?