I searched on Family Search for a Dugdale that lived in Carthage and found the marriage record of a William Dugdale, the son of William Dugdale, to Martha Allison, the daughter of Thomas Allison.
One secondary source of the existence of Michael Plunkett is the divorce record of Nancy Doran from Martin Melvin.
Martin's statement reads:
Hancock co, IL, Circuit Court, Box #171Martin Melvin vs Nancy Melvin—In the Hancock Circuit Court at the March Term A.D. 1862“Your orator Martin Melvin here represents and shows unto your Honor that heretofore on the 10th day of December AD 1862 the said Nancy Melvin filed her bill on this court praying for a divorce from your orator Your orator further represents and shows unto your orator that heretofore to wit on and before the date of the pretended marriage with your orator as set up in the Nancy Melvin bill before mentioned the said Nancy Melvin was married to Micheal Plunckett who was living at the time of said pretended marriage and is still living as your orator and defendant has been informed since said pretended marriage and he lives in the state of Ohio. And your orator was ignorant of the existence of said marriage of said Nancy when said [word?] marriage occurred. This defendant further shows and represents unto your Honor that the said Nancy Melvin since said pretended marriage has treated your orator with continued and repeated cruelty by striking this defendant & pulling his hair & cursing and abusing your orator & by abusing his children on various times & occasions since the first day of August AD 1860.Your orator asks that the said Nancy Melvin may be compelled a full true & perfect answer to make to this your orator’s bill and that upon the final hearing of this cause that your orator may have a decree of this Court dissolving the pretended bonds of marriage between your orator & the said Nancy Melvin & that the same may be declared null & void & that your orator may have such other & further relief as in Equity he may be entitled to and as to this Court may seem meet and he will ever pray.Martin Melvin by his solicitors Mack & Draper”
Nancy's reply reads:
Muddling through the legalese, you can see that Nancy was married to Michael Plunkett and that Nancy says that he died more than seven years before her marriage to Mr. Melvin, which occurred in 1860. This puts his death at 1853 or before if Nancy's statement is true.Martin Melvin vs Nancy Melvin — Hancock County Circuit Court March term 1862, Cross Bill“the separate answer of Nancy Melvin cross Bill of Martin Melvin filed in the Hancock Circuit Court March term 1862 this said defendant now and at all times hereafter saving to herself all and all manner of benefit or advantage of deception or otherwise that can or may be had or taken in the many errors uncertainties and imperfections in the said Bill contain for answer thereto …that so far as to her having a husband alive at the time of the marriage with the said Martin Melvin is utterly untrue and false but on the contrary she says that her husband had been dead for more than seven years before her said marriage with the said Martin Melvin that she denies having at any time used either cruelty by beating the defendant or pulling his hair or any manner [word?] beating him she denies abusing his the said Martin Melvin's children but on the contrary treated both he and his children with all the respect due to them this defendant denies all and...
Based on Thomas Doran's age in the 1860 US Federal Census, six years old, it seems likely that Thomas was born in about 1853 or 1854 as it states his age is six years old at this time.
Based on the supposed date of Michael Plunkett's death and the approximated date of Thomas' birth, it is possible that Mr. Plunkett could be Thomas' father. Finding a DNA match to a person with the surname of Dugdale, who is descended from a Plunkett, is quite intriguing. Added to the fact that there was a Dugdale, which is not too common of a surname, living in the same town as my unmarried great-great-grandmother and things get interesting.
No, nothing is certain at this time but this collection of names all associated with either a DNA match and/or being located in Carthage, Illinois and/or with being married to my great-great-grandmother, gives me a sense of hope that the identity of the father of my great-grandfather might eventually be discovered.