I think you can assume the Parish paid for the baptism, so it was entered into the Poor book.
There is a general consensus that baptisms were free in those days, I fear not.
3 to 6 old pennies would possibly been the cost, which I have found in the parish registers. Not sure where the payment eventually ended up though.
The Poor book, is usually an account book, for Poor relief, administered by the Parish. An early form of Social Welfare and payments.
Poor houses were also a part of the set up, not saying you needed to be in one, to get poor relief for a baptism.
https://en.wikipedia.org/wiki/Poor_relief
Steve.