annie’s room, n. — Green’s Dictionary of Slang

annie’s room n.

In phrases

in annie’s room (also up in annie’s room) [orig. milit.; used in darts to denote the throw of ‘double-one’, considered the least attainable double on the board]

(Aus.) a phr. used in answer to the question ‘Where is...?’ when the respondent does not actually know.

1921		(con. WWI) E. Lynch Somme Mud 104: When I enquire of the O.C.’s whereabouts someone replies, ‘Up in Annie’s room.’ .
1924		(con. WWI) A.G. Pretty Gloss. of Sl. [...] in the A.I.F. 1921–1924 (rev. t/s) n.p.: ‘Up in Annie’s Room,’ – facetious answer to questions as to the whereabouts of someone who cannot be found.
1925		(con. WWI) Fraser & Gibbons Soldier and Sailor Words 7: Annie’s Room, In: An expression by way of jesting answer to an enquiry for someone who cannot be found.
1982		N. Keesing Lily on the Dustbin 83: Had Christopher Robin been an Australian child the answer to his plaintive query, ‘Has anyone seen my mouse?’ might have been ‘It’s up in Annie’s room behind the clock.’ Variants [...] are ‘Up in Annie’s room resting on a pedestal’ or ‘hanging on a cobweb’.