The US 1880 census holds two entries for manx-born Quiggin(')s:

The first is John J. Quiggin, a Blacksmith aged 40 born IOM. His wife Susan J Quiggin is aged 37, born OH with a German father. Their two daughters are Anna M. aged 14, born in IA, and Ada M. aged 15 also born in IA. This record is from 'E.D.76, Cass, Guthrie, Iowa', Family History Library Film 1254342, T9-0342,65B.

The second is John J Quiggins, a machinist aged 31 born IOM. His wife Ellen is aged 21 born OH, and their two sons are George aged 4 born OH and John T. aged 1 born OH. This record is from Cleveland, Cuyahoga, Ohio, FHLF 1255008, T9-1008, 250B.

It seems that Harry wasn't around in 1880, but maybe you can match this up with his siblings. Take a look at www.familysearch.org if you want to explore more.

Good luck,
Jon