Clive suggested the following in note below.
QUALE, Anna d/o Thomas QUALE & Anna chr 07 may 1871, Douglas, St Mathews, IOM 
Possiblt dau of: 
Thomas QUAYLE m Ann WADE 09 Nov 1861, Kirk german, IOM 
Other offspring: 
QUAYLE, Thomas chr 10 may 1868, Douglas, St mathews, IOM 

She may indeed be the above Anna.  However, I have recently learned that Thomas Quayle and Ann Wade are another Quayle line entirely and lived in Patrick Parish.  I'm not sure who the Thomas and Anna who are the above noted parents are.  Thomas may have died before 1881.

1871 Census Index
Douglas 6 50
Quayle
Thomas 29 b Michael
Ann 28 b Patrick
Thomas 2 b Douglas

1881 Douglas
Douglas 1881 District 5 page 28 of book #296 -  6, Hanover Street:
Ann Quayle head married age 40 Laundress born Patrick
Thomas Quayle son age 12 scholar born Douglas
Anna Quayle daughter age 10 scholar born Douglas