Green’s Dictionary of Slang

(Aus.) to get married; to initiate a relationship.

1915		Bulletin (Sydney) 5 Aug. 47/2: ‘Where’s the cliner?’ / ‘Oh, she’s hitched it with Bill Wilson.’.
1985		‘Thommo’ Dict. Aus. Swearing & Sex Sayings 67: HITCH IT — The start of a new relationship between two people as lovers or bed mates.