In answer to your question, yes you can do this. However you will have to follow these steps:
1. Select all of the elements on the page you wish to extract.
2. Using the selection tool, drag all these elements (picture frames, text frames etc) as one selection to your desktop ( bare with me I'm going somewhere with this)
3. There should now be a new file on your desktop with the extension .inds, this is a Indesign Snippet file.
4. Create a new document in InDesign to the specs you need (should be the same as the file you are extracting from).
5. Drag the ".inds" file from your desktop to the new page you have created.
This will now place those same elements onto your new page. Now your probably asking why did'nt I just copy and paste... well the beauty if snippets is that you can drag single pages or a spread using the same action and use at your convenience. Only downside is that Indesign will only allow you to select multiple elements from the same spread, you cannot select a series of elements across multiple spreads (hopefully they will have fixed this in CS3).