You should never try to RUN QB from Dropbox, Google driver, etc., but saving a backup to it, downloading when needed, restoring, working, then backing up again is fine.

https://betterbottomline.com/dont-try-to-run-quickbooks-pro-premier-or-enterprise-via-dropbox-google...

Your license allows you to install a single user license on up to two computers (the intention is that it is to be used by one person), but you cannot configure the two computers for multi-users.  You will have to back up from one, restore to the second, then back up from the second, restore to the first (never using the backed up computer in the meantime), etc., which can open the door for problems if you inadvertently work in the backed up computer while the other is in use.  You might want to consider a remote access program like LogMeIn,SplashTop, JoinMe or  TeamViewer, designating the desktop as the host and the laptop as the remote computer (you don't even need QB on the remote computer as you work in the host QB) or have your file hosted (Intuit now offers that service) so that you can access it online from any internet connection.