Dragging from desktop to laptop

Your Desktop is already on your computer. I think you mean to drag a webpage from your browser to your Desktop. If you go to the Save As option under Safari's File menu you can save the open page as a Web Archive or as an html source file. If you select Print from the File menu, then you can select Save as PDF from the PDF dropdown menu. What you cannot do is actually drag the page to your Desktop.

Why not just Google, Yahoo or Bing the same website on your macbook...?

AuLwEsXe wrote:

... can I just drag an open webpage over from my iMac screen to my Macbook's?

The short answer is no. The longer one is there some convoluted ways to do this like by using screen sharing over a network but they are cumbersome, slow, & not really the same thing as opening the page on the MacBook using its browser.

Without knowing which version of OS X you are running on each Mac it is hard to make specific suggestions for workarounds but considering what you want to do you might be interested in trying out Teleport, a donation-ware utility that allows you to control two Macs using one keyboard & mouse. One of its features is allowing syncing of the "pasteboards" (the clipboard) of the linked Macs, so with that feature enabled you could copy the address of the web page displayed at the top of the browser (the URL) to the clipboard on the iMac, & then paste it into the address bar of the open browser window on the MacBook. Hit return on the MacBook & the page should load from its source, just like it did on the iMac.

No. But if you have both connected to your local network you can copy files from one computer to another via File Sharing or Screen Sharing. You can email files to yourself then recover the attachment on the other computer. You can use a service like DropBox to transfer files via the cloud (not iCloud.)