Tipperary North Riding and South Riding have separate genealogy records on line with a not for profit but fee paying website: www.rootsireland.ie
If you have both parents names you should be able to find a birth certificate available from: www.groireland.ie
I thought perhaps Alice would be at someone else's house in 1901 but doesn't appear to be an Alice of the right age listed as a visitor. She certainly didn't pass away as she appears in 1911. There are other possibilities such as being put in an orphanage temporarily if the family was in dire straits. Perhaps she was out of the house at the time of her families census but not when the family she visited
when their census was done. A census take couldn't be everywhere at once. Its hard to say why.
The census substitute Griffith Valuation took place in Tipperary in 1852 probaby the parents of your parents!
Ancestry's Irish collection is limited although better than it used to be.
As the births are after 1864 you should be able to find the civil registration free on www.familysearch.org
but not always are the parents listed with the children.
I might be able to find Johanna Barrett's 1863 parents as long as she wasn't the youngest in 1864. I have births
on CD from 1864-1875 only. The letter C no longer works.