Ok, I will assume here that you opened two images each one is in its own document. Clicking the tabs at the top of the screen switches between the two documents and both image have only a single locked background layer.
You are correct in saying select all, copy, then paste. That is one way.
However with the move tool active (lowercase v on keyboard) You can place the cursor over the image hold down the mouse button and drag that image to the other tab. While cursor is on top of that tab (you are still holding down on the mouse button) the documents will switch. At this point you can now drag to the center of the document and finally let go of the mouse button.
If that does not happen, please post a screen capture of your screen so we can see how you have photoshop set up. As it is possible the tabs are not visible for example.