Agnes may have been sent to Brisbane by her family for the first birth, however it's still possible that her future husband (George Martin) was the father of all the children. This is only conjecture, but the births are spaced every 2 years, in the normal pattern for the era. There may have been some reason for them not to marry until after the birth of Vivian.
Let's try and deal with facts. We have no proof that George was the father of all the children. They are not mentioned on Agnes Maria's death certificate and IF her husband was the father I would think they would be acknowledged as "their children" whether born before or after the marriage.
In 1899 Agnes
McMAHON, 19, born Amarac was of
Breakfast Creek not Ipswich when she certified in writing the information on the birth registration of Kevin Hamilton
McMAHON. In 1903 Agnes' father Michael and step mother, Agnes Mary were living in
Gladstone. There are some earlier rolls for Qld but I don't have access to them. I referred to church homes for unmarried mothers in Ipswich earlier in the thread, perhaps these should be followed up.
Name does not change. Maria Agnes was her registered given name on her birth and death notices however on the electoral rolls she chose to enrol as Agnes Maria. I would suggest that Agnes Monica was possibly a mistranscription. I would suggest she chose to be known as Agnes. It is not unusual to only see a parent's first given name on registrations and indexes.
I think you are waiting for a marriage cert for Ellen.
Cando