QR codes are completely passive. They do not collect any information about the devices used to scan it.
If you want to set this up using only the Bitcoin network, you can create QR codes with private keys of Bitcoin addresses. The device used to scan the code should be able to import the private key and send its bitcoins to another address chosen by the user. The user should destroy the QR code afterwards to avoid stealing attempts by other users.
Having a "pool" of bitcoins in a QR code is not possible in this scenario.
Since mobile clients currently can not import private keys, another easy way to do this would be with Instawallet. People would scan an Instawallet QR code, open the url, type in their address and cash out the bitcoins.
But again, this solution does not allow for a bitcoin "pool". If you really want that feature you should design a dedicated website, like David Schwartz suggested in his answer.