I don’t use Alfred, so I can’t tell you how to use it to run an AppleScript, but this is (approximately, at least) the AppleScript you can run:
tell application "Google Chrome"
set theURL to URL of front window's active tab
get theQuote & linefeed & linefeed & theURL
This gives a plain text result, with the quote followed by a blank line and the URL. You can jazz it up with Markdown or HTML as you see fit.
As you can see from the last line, the output is left just sitting there. I don’t know how to make a new draft directly, as there appears to be no AppleScript dictionary for Drafts.
If I needed this ability, I would use Keyboard Maestro to run the script and paste the results wherever the cursor is (presumably in some text editor). Chrome doesn’t have to be the active app for it to work.