I don't think Birkenhead would take kindly to being described as a suburb of Liverpool.
Didn't the Beattles sing something about it?

I can find two possibilities in the 1861 census, both aged 6.

Isabella the daughter of William & Ann in Ramsey is in the 1871 census, so I guess not her.

1861, German, district 2, schedule 54, Ballalace
Isaac Cannell, head, married, 33, farmer of 130 acres, Braddan
Catherine, wife, married, 27, Jurby
Thomas E, son, 6, Braddan
Isabella J, daughter, 6, Braddan
Emma, daughter, 2 months, German

In 1871 Catherine is a widow. Thomas & Emma/Elizabeth are with Thomas & Ann Cowin, on a 127 acre farm at Ballaleece. This looks like the same property as the 1861 census, and they are described as nephew/niece.

I can't find Isabella J which would be consistent with her having moved to England.