Posting in the Magento forums has been disabled pending the implementation of a new and improved forum solution which should better serve the community.
For new questions please post at magento.stackexchange.com, the community-run support site for the Magento community. We will be providing updates on the new forum solution soon. For questions or concerns please email email@example.com.
Normally the developer will allow you to use the same extension for both your development and live website. All our extensions are sold like this.
As SeL says, you should check with the developer first. If they say you need two licenses, make a complaint and point out that best practice web development requires at least a development and live website (and possibly a staging environment too).