Hi Katie -
Yes, Quine certainly is a Manx name.
Quine's Hill is in Kirk Braddan parish - near Douglas - but is thought to be a modern name (from JJ Kneen's Place names of the Isle of Man) - but there is a Ballaguine (Quine's farm) in the same parish that has been called that since 1511 (at least). There is a Ballaguine in Lonan parish too (from 1703)
My mother's family name was Quine - they came from Douglas.

Roger