Unfortunately, it does not appear as if the HP 4580 is AirPrint compatible. Check the list in the link below to verify:
If your printer is not on the list, you still might be able to set up printing from the iPad by installing an application like Printopia on your Mac. There is a free trial, so you will know in a few minutes whether or not this might work for you. You do have to have a Mac running on the network in order for Printopia to function correctly.