A fine copy published in 1872 (Carroll wrote it in 1871) sold recently on E-bay for just under $1,900 (US). It was, however, paired with its sister book What Alice Found There.
A similar pair, but including a verified hand written card in each signed by Lewis Carroll is on the market for $15,000.
It appears difficult to find a stand alone first edition of Alice: Through the Looking Glass.
Caution is advised concerning the title of any Carrrol (pen name for Charles Lutwidge Dodgson) work though. Originally published as a sequel to Alice's Adventures in Wonderland(1865)(Original title: Alice's Adventures Under Ground) Through the Looking-Glass and what Alice Found There (1871) has been published with many variations on the title, check closely and best of luck!