I'm assuming that the printer shown already installed on your laptop was the result of plugging the printer directly into the laptop, and not the network version of that printer which is USB-attached to the XP desktop and that you're trying to install on the laptop.
Ok. It's the "access denied" error that we need to overcome. Some kind of a network password issue perhaps.
Do you have a user/password defined for both laptop and desktop?
Are the drives of the XP desktop accessible directly as drive letters? In other words, can you "map network drive" for a partition on the desktop, from the laptop? Or, if you try to "map network drive" for an XP drive to a Windows 7 letter, do you also get "access denied"?
Can you even see into the drives of your XP desktop from Windows 7, other than those specific "share" folders?
Your screenshot shows a bunch of "share" items on the network, along with the printer, but these may be folders on the desktop machine that you specifically "shared".
Can you post screenshots from the XP machine, of what your printer definition looks like on that machine?
For example, on my own XP partition here is what my USB-connected printer looks like, if you right-click and select Properties, and then select the "sharing" tab, and then push the "additional drivers" button to show what's installed.