I can see Edward's mother Agnes using the name MEIKLE on the electoral rolls in Queensland where she is living with Edward's wife Elizabeth Edna who is also using that surname. No sign of Edward but perhaps he just wasn't registered to vote.
Agnes died in 1914, parents listed as Edward COLEMAN and Bride (Bridget/Bridie?) CRONIN.
I think these two newspaper articles refer to your Agnes - the first is an argument with Charles DIX in 1889
http://trove.nla.gov.au/ndp/del/article/76976475 and the information given there leads back to this story in 1887
http://trove.nla.gov.au/ndp/del/article/78587670 and the death of Agnes's husband James MEIKLE on November 6th
1887
C2053
James MEIKLE
Father:James MEIKLE
Mother: Margaret ADAMS
If you search for just the word MEIKLE and narrow your search to 1887 you can follow other stories and letters to the newspaper. The Charters Towers burial register shows that James was aged 52 and the cause of death was Hepatitis/Gastritis.
http://www.charterstowers.qld.gov.au/documents/41682213/4172...This is likely to be their marriage in Victoria:
Name: James MEIKLE
Spouse Name: Annes COLMAN
Registration Year: 1874
Registration Number: 880
I see a number of family trees on Ancestry have Edward's year of birth as about 1863 at Geelong - is that correct?
If so, then the relationship with CARTWRIGHT was earlier. Because she married as COL(E)MAN, she may not have been married when Edward was born.
The burial register gives Agnes's age as 73 in 1914 so born around 1841 - plenty of time to have a nice complicated life before she married James in 1874!!
I think that marriage cert would be my first purchase, just to find out more about Agnes (where she was born, confirm parent's names and her status). You can purchase an uncertified image online and download once you have paid.
Her death certificate could be worthwhile if Elizabeth Edna was the informant. They had been living together for some time so she may have known the full story, but it probably just has the info you already have of Edward's father being named Thomas. You should however get the names of any other children she had.
Debra