Laura - I think I may have found the family you seek in the 1901 and 1911 Census in Ireland - this is a free resource hosted by the National Archives of Ireland and is very useful for tracing Irish family history!
Bridget Dodd appears to reside in Killarney in 1911 and is just six months old. Her siblings in the house are Robert (15yrs), Hannah (12yrs), Eily (8yrs) and Willie (5yrs), but only one parent is listed - her 'father' 'Ellin' - I think two mistakes have been made here - the census enumerator listed the only adult in the household as a male by mistake and the modern-day transcribers read 'Ellin' instead of 'Ellen'. To prove this - follow this link:
Check the 'Household Return (Form A)' to see the basic data - see how the census enumerator has crossed out 'widow' and written in 'married' instead - perhaps Ellen told him her husband wasn't dead as he assumed firstly, just working away from home at the time!
Then look at page 2 of the 'House and Building Return Form (B1)'- see line 24: the name certainly looks like 'Ellen Dodd'.
To get more information, step back ten years to 1901 and check the same address - now we find Ellen Dodd (female, of course) living with her husband Henry (a boot & shoemaker) and her children John (8yrs), Robert (5yrs) and Hannah (1yr), so it is almost certainly the same family as we saw in 1911, though of course Eily, Willie and Bridget haven't yet been born in 1901 and John isn't present in the house in 1911.
Follow this link and then click 'Household Return (Form A)' to see the original census return:
To go one step further and look in the Ellis Island records, a certain Henry Dodd (a shoemaker...) passed through Ellis Island with his sixteen year-old son John on May 21st 1910 (thereby missing the 1911 census in Ireland...), having left his father James behind in High Street, Killarney (not sure why he didn't list his wife here...). He was going to his sister-in-law Mrs Sullivan at 18 Cubbage Street, Carnagie, PA, but perhaps he went to Canada from there and eventually brought over his wife Ellen and his remaining children?