Cany I Copy dng files from one computer to another....

Question

...without losing the editing I've done in the develop mode?  I don't want to move them, just copy them.

Answer 1

That's one of the big benefits of the DNG format, Pixeltaker.  All your LR edits can be stored directly inside the file.
LR is a database driven application, so the database is the first place it stores all your edits.  LR can be told to also store the exact same information automatically inside your DNG files, but it's not configured for this out-of-the-box.  To insure the edits are written into the files themselves, you can do one of three things:
Before copying the files to another location using (Win) Explorer or (Mac) Finder, select every file in the Library module and press Ctrl (Cmd) - S.  If you have hundreds of images, you'll see a progress meter appear in the top bar while it "saves" all the changes logged in the catalog to the DNG files.
Alternatively you could use the LR export function to select all the files you wish to copy, and use the export as DNG option.  This will create a second copy of the files in a new location of your choosing, and the new files will contain all the edits.
As a third option, you can go into the catalog settings of LR, and on the Metadata tab check "automatically write changes into XMP."  This basically tells LR to automatically perform step 1 to every DNG/RAW file live as you perform the changes.  This will also apply retractively to any files in the catalog which have been changed, but not written to the files, so if there are many you should expect LR to grind away for a bit after enabling this option.  There are some circumstances where this may have an impact on your computer's performance.  When working on one or few files at a time, the live updating of each file will happen seamlesssly with no noticable impact.  When adjusting hundreds of files at once, you may notice a slight performance degredation as every file is touched by LR with every single change.  The degree of the impact really depends on your system, and the performance of the drive containing the RAW/DNG files.  Many photographers (myself included) feel this option is the most convenient, and the tradeoff is well worth the occasional slowdown.  With this option enabled, you could go straight to the master files and simply copy them to your new location, and all the changes will always be there.
If you have non-DNG RAW files, LR will instead save the changes into a sidecar XMP file, as the proprietary files created by the camera manufacturers do not have a space designated for logging your edits.  This creates two files to manage while moving files around, so I much prefer DNG for simplicity.