Another census in Ireland that has survived all the unfortunate events of the early 20th century is the 1911 census. It is a very interesting census and includes a little more information that the 1901 census including how long the married couples have been married. This really helped me to nail down that this was indeed my ancestor.
What it tells you is:
Relationship to head of household
What was particularly fascinating for me was that my relative spoke both Irish and English. There was a rumor in our family that my ancestor Johanna Connors Donahue was a Gaelic speaker and now I know it is likely true since it is likely that her husband Cornelius also spoke Gaelic since his brother did.
The Irish census is available at the National Archives of Ireland website.