Quick way to find a specific email in Thunderbird inbox?

You could and should use Message-ID field in the header. To be able to find it easy just customize your search.

Go to Edit -> Find -> Search Messages. From the search field select the last option "Customize ...", in the text box of the new apperead Window write Message-ID and click Add and then OK ( tested in Thunderbird 11.0.1).

Now you have a new field to search by, select it write your ID in the search field and Voilà.

I do this to connect a "TODO" list with an email. The search is reliable and faster than "From+Subject".

I just wish I could add this to "Quick search...".

The ThunderLink plugin provides a custom thunderlink://messageid=... protocol handler. With the plugin, you can put such a URI of the current email to the clipboard, and use that in TODO lists, web links, etc., and a click / invocation of that link will immediately get you back to the email in Thunderbird!