There are two what look like Wood illegitimate children born in the Liverpool area in Q1 1901, districts being Liverpool, West Derby and Toxteth Park. Both were born in the West Derby district. We can probably forget about George Wood as he appears to be on the 1901 Census with his mother a domestic servant and her sister's family:-
www.familysearch.org/ark:/61903/1:1:X92N-CZK
That leaves the Male Wood child as the only candidate if we are looking for an illegitimate born Wood child in Liverpool in Q1 1901.