How can I download the desktop version and keep it synced with my online?
You cannot. QBDT and QBO are not meant to be run concurrently, it is either one or the other. If you want online access to your desktop version, consider having your QB hosted in the cloud. Intuit now offers that service, as do many others.
You have clicked a link to a site outside of the QuickBooks or ProFile Communities. By clicking "Continue", you will leave the community and be taken to that site instead.