I want to download KSP 1.0, but it says I have to purchase it. I have already purchased KSP before the update.
No, if you've purchased the game already, you don't have to purchase it again. If you bought it on Steam, or have transferred your purchase to Steam, your game will be automatically updated.
If you bought the game through kerbalspaceprogram.com, you can download the latest version by logging into the store, and then clicking on the My Account link. Alternatively, you can open the KSP launcher and click the Update button. Enter your account details, and it'll take care of the rest.