This is what I have found in the Kirkeby, Sunds, Svendborg church records.
Mette Kirstine Rasmussen was born on 17 Jan 1840, parents weaver Rasmus Jensen and his wife Anne Hansdatter, opslag 36 nr 1.
Her father, Rasmus Jensen, age 36, died on 29 Mar 1840, opslag 137 nr 2.
Mette Kirstine Rasmussen married Anders Jensen, age 42 and a day laborer, on 7 Mar 1862, opslag 104 nr 2.
Her mother, Anne Hansdatter, age 65, died 2 days later on 9 Mar 1862, opslag 104 nr 2.
Anne Hansdatter left Kirkeby with her husband on 18 Mar 1862, desintation Vejle, Jylland, opslag 146 nr 2.
Here is the Danish record of her emigration for Queensland, Australia.
Name: Rasmussen, Mette Kirstine Occupation: Pige
Age: 32 Destination: Queensland
Contract no.: 194800 Registration date: 4/12/1873
Last res. parish: Rudkøbing Last res. county: Svendborg
Last residence: Rudkjøbing Destination country: Australien
Destination city: ? Destination state: Queensland
Name of ship: Indirekte
Not that she is listed as a pige which normally refers to a girl who has never been married. My guess is that her husband has already died and she does not have any children. She probably left Denmark because she was always poor and was seeking a better opportunity.