I noticed that Minnie's parents didn't marry until 1889
Marriage Reg # 1889/2921 Jessie Morrison married James Mackie
Would it be possible that the children were registered under Jessie's maiden name. Did Minnie have any siblings?
Birth's NZ - could Mary Morrison be your Minnie Mary MACKIE (Minnie can sometimes be a nickname for someone called Mary she may have just kept it???)But seeing as her parents didn't marry until 1889 I would be inclined to look at the MORRISON births.
1879/15300 Morrison Mary Mother: Jessie Father: NR
1881/16911 Morrison Eva Mackie Mother: Jessie Father: NR
1883/2824 Morrison Ellen Mother: Jessie Father: NR