I can see four workhouse admissions that may be for Kate, all under name "Catherine," between 1900 and 1904. They have different addresses, and ages, so not clear that they are all the same person.
01/04 to 4/5/1900, age 23, address 5 Doluns(?) Petersons Lane
Reason for admission - Dr. Garand's note. Arrested at Chancery St. Dispensary PC 203D
[Latter is presumably policeman's ID number]
9/2/ to 3/5/1901, age 20, address Kingstown, reason pregnant. William born during this period.
5/11 to 12/11/1904, age 26, address Bray, reason pregnant.
15/11/1904 to 2/5/1905, age 26, address Bray, reason pregnant. James born and died during this period.
If the first admission is Kate, then I think it reasonable to suppose that she may not have known the identity of the father.