is it as simple as clicking on sync to this catalog on the laptop and then doing the same when i get back desktop.
i dont want to screw things up when i get home to my Desktop computer
No, it's not that simple at all. As you can sync only one single catalog, what you want is not going to work. Each time you sync the 'non synced' catalog, the other catalog sync is terminated and the online images are 'orphaned'. As a result, the newly synced catalog is going to see them as new images and will download them all as such. You'll create a mess.
The way to do this is either by using a catalog stored on an external disk that you carry along, as @F. McLion suggested, or use 'Export as catalog' and 'Import from another catalog' to keep your desktop and laptop catalogs in sync.