Did the Shire have post-offices?  or is this the voice of the translator JRRT naming a familiar place because Bilbo named something which the audience would have no idea about?

• 04.017 as well as you do to the nearest post-office;

Hyphenated or not, according to OED.

“post office, n.” OED Online, Oxford University Press, June 2017, http://www.oed.com/view/Entry/148624. Accessed 19 September 2017.