Good and bad news I'm afraid...

The good news: I found the baptism at Rushen Parish Church on 12th January 1878. If Annie Isabella had been born in December 1874, then she was 24 months old when baptism, which is a little unusual, but not impossible. The entry is on Page 172 Entry No. 1376.

Rushen
12th January 1878
Annie Isabella
illegitimate daughter of Annie Quirk
of Struan-snail.

Bad news: the father is not named.

Struan Snail is listed in George Broderick's Place-Names Volume for Rushen. Struan = Stream. The Snail bit is not so clear, possibly from an Old Norse word mean 'steep' or similar.
It is apparently a stream which runs from Mull Hill (above Cregneash) across to Port Erin Bay.

Note: An 'Adelaide Quirk' was baptised at Rushen on 25th December 1874. Daughter of Robert Quirk [a Tailor] and Catherine (nee Watterson) of Port Erin.