Can I purchase the single license to use on a development site and then transfer to the new site once live?

Yes absolutely, you can develop the website on your development/test server using the single plugin license.

Then once you go live just log-in to  your account and change the old development website  url  to the new website  url  and the new site will be using that license. Swapping activation keys are handled from your account.

Once the new website is active, you will be able to update your extensions from the WordPress dashboard and get support for it.