Mona’s Isle is another name for the Isle of Man. In the Clague collection it is attributed to Henry Kitchen (1802), although it isn’t clear whether he was the composer, or whether it was collected from him. 1802 was well before Clague began collecting anyway.
Mona’s Isle Quickstep
It’s generally thought Clague (Dr John Clague, folklore collector in the Isle of Man during the late 19th Century) copied it from another music notebook and not much more is currently known about it. It does illustrate the fact that in the Isle of Man, as elsewhere, more types of dance, and dance tune, existed than is reflected in most sessions today.
I’m not sure about "Mona’s Isle" being another name for the Isle of Man, or, if it is, it’s only in the same way as "Paddy’s Green Shamrock Shore" is another name for Ireland. You wouldn’t find it on an airline schedule (though it’s amusing to think it might appear on screens in airport lounges!).