Hi Amanda,
Sometimes if a child had died the parents would give another child the same christian name. I think this was the case with your Mary b1910 because there is also this one.....
Mary Walker baptised 27 June 1902
Purston cum South Featherstone, St Thomas
Parent's Andrew and Mary Walker
Again it was a private baptism
There is a possible death record June Qtr 1902 9c 81 Pontefract
If this is correct then she must have died very soon after the baptism.