ucan,
Let me start by making it clear that I am not an expert. However from my experience reading DV stuff I know that as long as you have completed a high school degree (some embassies might also require at least average scores) you can apply on your own regardless of your age. But if the main applicant (e.g a father/mother) includes his/her children in the application, the children can qualify to travel with the parent if they are unmarried and they had not yet reached 18 years of age by the time the parents applied for the DV Lottery.
For more info check out page 11, (item number 20) in the instructions pdf in the link below:
google ....... travel.state.gov/pdf/DV_2013_instructions.pdf ....... (couldn't attach the link)
In fact, if possible read all the information contained in the above document carefully these are the official application instructions for DV 2013.
Best of Luck