Hey,
I'm not sure I understand the problem. If you just draw a marquis with the selection tool around just the items on the page, you should be able to copy paste that to a new page. Now if something on the page you want to copy is also on the facing page you don't want to copy, your marquis selection will select it as well. You'll have to adjust that page item so it is only on the page you want to copy from.
Another way to go about this: Under the Pages submenu, deselect "Allow Document Pages to Shuffle" and select "Allow Selected Spread to Shuffle". Then in the Pages panel, target just the page you want to move and drag it to its new location. If this new location is the opposite (say you're moving a verso to a recto), ID may reapply a master page to it.
Hope that helps.
Greg Ledger