Ahh, yes you can...
I started my business (registered with the Gov) when i was 16. Atleast thats the law in Australia.
The best thing for you to do now is read up heavily on business practises and marketing, etc. Its more important that you have a firm understanding of how Internet Business operates apposed to the technical knowledge. Your skills wont be very handy if you dont know how to attract and secure clients! Though, technical knowhow is an important factor, also.
www.sitepoint.com offer a fantastic box-set, which goes into details about how to start a Web Design Business (rather pricey, though).
Go to some of the local clubs, churches, small business's, etc and offer to write them a simple Web Site for a small fee (or for Free!). This will build your design portfolio, and experience.
Be confident when it comes to attracting business. Potential clients dont need to know your only 15! I got a contract to write a database-driven Events Calendar when i was 16. As long as you can provide the service professionally, the rest is secondary.
I will move this thread to the Business forum.