You need to look at File > Export as Catalog, and on the other computer File > Import from Another Catalog.
Yes, that's what I do.
Or, it can be simpler if your laptop connects at home to a network with your desktop.
From your desktop (with the laptop online on your home network) in LR simply do "Import from another catalog", and navigate to the folder on your laptop containing the LR catalog. You can then pick out the folder and photos you want to import across to your desktop.
It can be bit of a fiddle getting stuff to go in the right folder on the desktop, but it's dead easy to drag and drop the folder to the right place if it gets put in in the wrong place.