Oh I do not think I would copy an image from InDesign and then into Photoshop. To me, that is about as bad as trying to copy an image from PowerPoint or Google Docs and then trying to paste it into Photoshop. It just does not work out well. No offense.
What I would recommend doing is saving all your images on a external hard drive and making sure they are dated and named with something relating to the original design.
Or or or or.... this is even better in InDesign.
Go to FILE and then to PACKAGE. This will save all your images and assets into one Folder. I almost forgot about this. This will take everything and save it one spot. This is really smart if you are working with teams, then you can send the InDesign file along with the Package to the other person. This even included fonts that you might have uploaded! I so almost forgot about this feature.