The above method stopped working with 1Password 7 because 1Password mini no longer exists. Here's an updated AppleScript which should help others.
open location "onepassword://extension/search/{query}"
tell application "System Events" to tell process "1Password 7"
set frontmost to true
delay 0.7
key code 48
delay 0.2
key code 124
delay 0.2
key code 125
delay 0.2
key code 36
end tell
Basically this opens the "mini" like app that actually runs as an extension in the main 1Password 7 process, inputs the query from the first object (or you can hard code it to search for a specific app), sends the tab key code to select the first search result, sends right arrow to select the username, sends down arrow to select password, and sends return key to copy it to the clipboard.