I always set up labels/colors for every camera and media type in my beginning setup for every project.
WHEN I take a selection of clips from the timeline and drag them into the Project Browser to make copies in a new folder, the labels do not carry over. They default back to the default label colors. This doesn't happen when copying from the Project Browser into Project Browser (itself).
Seems to me like a bug.
Perhaps there's an option or modifier key to actually do this.
To repeat this for yourself:
Label some clips various colors in the project browser
Drag them into a timeline
Select all of them and drag them back into the project browser and make sure the cursor has a + sign next to it so that it is making alias copies
Note the label colors of the newly copied versions in your project browser