Are you saying that your ancestor's parents were not married but a father's name was given on her baptism certificate? This man, named as the father, married another woman the following year?
If so, perhaps he was her father. Fathers were sometimes named when a child was baptised.
As to how the mother supported the child, that would depend on a number of factors such as did she have support from family or the parish, was she able to work and provide for the child, was she of independent means, plus other considerations. She may have been in a better position as a single mother of one child, than a married couple with many many mouths to feed on a low income.
Others will probably have more ideas for you.