The only way to transfer flags from one computer to another is to use File->Export as Catalog on one computer, transfer the catalog and photos, and then on the other computer use File->Import from Another Catalog.
If you are going to do this, don't delete the photos from Lightroom or from your hard disk until you complete the transfer. Then, on the laptop, you can delete the photos from Lightroom, or delete photos from both Lightroom and the hard disk, your choice.
Reading between the lines, I get the impression you want to delete the photos from Lightroom on the desktop after you upload to Facebook or create a photo album. My advice is to not delete from Lightroom on the desktop and do not delete from the hard disk. Leave your photos in Lightroom on the desktop! That way your edited photos and flags and other metadata are always available. Once you delete from Lightroom, your edits are gone, your flags are gone, and I can't recommend this.
Actually other way around. We work on our laptops most of the time and that's where we do our editing/uploading etc. So we want to delete them from our laptops, which have limited space, but transfer flags/ratings to the desktop which would keep all the photos in lightroom. (Right now we are using google's picassa).
Yes, I understood that, and my advice is that once the photos are transferred to Lightroom on the desktop, you do not delete them from Lightroom or from the hard disk. As I said, this was reading between the lines, you didn't say you were going to do that, but just in case ...