Hi Hev,
A J. BORLAND aged 36, single, arrived at Port Chalmers on the ALHAMBRA via Melbourne VIC AUS. It departed that port on 7 March 1863.
This is the only record I could find, so perhaps the family was on one of the many immigrant ships that didn't call at Melbourne.
I concur with Mk2_Zephyr about working back from the known to the unknown, but have you checked the 1861 Scotland Census for her aged about 1? This might be a short cut.
Do you have any other information about her which might help? (Edit: She married Thomas John ANDERSON in 1882)
riley