You didn't say where in Pennsylvania Edward lived, when Rose was born or when and where they died, however, the 1910 census shows an Edward Duddy born ca 1874 in PA, wife Rose born ca 1879 in PA with several children living in Pittsburgh.
Oddly I could not find them in any other census under any spelling.
I did find an Edward Aloysius Duddy in the WWI draft registration records who was living in New castle, Lawrence Co., PA. He was born Feb 25th, 1877 and his wife was Rose.
The Social Security Death Index shows Rose Duddy who was born 23 Nov 1875 and died 15 Dec 1969 and last lived in New Castle.
Some of these records you can look at for free at labs.familysearch.org and Ancestry.com. For those you cannot see for free I suggest checking with your local libraries to see if they have Ancestry or Heritage Quest.