He also seems to be appear in the index to the 1861 census on FamilySearch as "Andrew Duggan", This might suggest a transcription error, but double check on the original image. The following screenshot is from FreeCen:
I checked FreeBMD, and found a death record for an Andrew Duggan in West West Bromwich in 1865. This is just before ages were added to the indexes, so this might not be the same man. However, if you are interested, the details are:
- Quarter: March 1865;
- District: W Bromwich;
- Volume: 6b;
- Page: 457
It may be possible to find Handy/Andrew Duggan in Ireland by tracing his children.
The Duggans have four children listed in the 1851 census who were also born in Ireland: Mary (born c1840), Margaret (born c1842), Anthony (born c1844) and Thomas (born c1847). [Note that "Anthony" may be transcribed as "Andrew" in the 1861 census]. The children were all born before civil registration was introduced in Ireland, so you will need to search church records.
The first thing to do is to check the original census images. Transcription errors are not uncommon when online indexes are created for censuses, and you want to make sure that you are searching for the correct names! You'll probably need to access these via a subscription service like Ancestry or Findmypast. If you are not already a subscriber, your local library may offer access.
Once you have confirmed the names of the children, a good starting point is FamilySearch, which has a good collection of church records from Ireland. Another place to try is the Church Records on the Irish Genealogy website. Both sites are free. If you are unsuccessful there, you'll need to check the Irish parish register collections on the subscription sites.