This hyphenated word is made from two common words.  Tolkien never uses “dining room” as two separate words.  We may be certain that in Bilbo’s native language there was a specific  – and probably important! – word for dining-room, not just some subcategory of “room”.  In the OED, this hyphenated form is the preferred spelling.

• 01.002 dining-rooms,
• 02.001 went into the dining-room.
• 02.002 in the kitchen before turning out the dining-room.
• 02.002 in the dining-room by the open window,
• 04.012 in Bilbo’s dining-room that seemed so long ago,

Just updating this entry to note that it’s a food word just as much as cellar or pantry is!

“dining-room, n.” OED Online. Oxford University Press, June 2017. Web. 7 September 2017.