The line is from East Lynne, a hugely popular play based on Mrs Henry Wood's novel of the same name, published in 1861. It does not appear in the novel.
But what did children call their parents at different periods in history? Mother and Father? Mama and Papa? Mum and Dad? Mater and Pater? Madam and Sir? Ma and Pa? Mummy and Daddy?
The best known - and most tear-jerking - fictional use of 'Daddy' is probably the one at the end of The Railway Children by E. Nesbit. And that line does appear in the book. It has a greater impact because Bobbie, Peter and Phylllis had mostly referred to their parents as 'Mother' and 'Father' to that point.
So when did Mummy and Daddy become commonly used by children?
A search of the records of the Old Bailey reveals the use of Mammy and Daddy from about 1730:
"Thomas Greneway, of St Giles's Cripplegate, was indicted for feloniously stealing a silver Tankard, the Property of Thomas Fletcher, the 26th of August last .
Mr Fletcher depos'd, That the Tankard being missing was search'd for, but not being found, his Wife and self went into the Children's Room, who were in Bed, a Child in Bed, about 7 Years of Age, cry'd out, Mammy, don't 'fright your self, I can tell you of your Tankard, I saw Greneway put it under his Coat."
"Thomas Robinson was indicted for stealing 33 pounds weight of bacon, value 20s, the property of John English Feb 17 
John English: I keep a chandler's shop in Wapping; last Wednesday was week, between seven and eight at night, I was gone into the back kitchen, my little girl that is about eight years old screamed out; I came into the shop; she said O daddy, daddy, the bacon is gone; I went to the hatch, and a boy told me he saw a man go with something from the window; I pursued as he directed; I saw a man under a lamp with something bulky; when I came under it, he, by looking back, had a full view of me; he made a sort of a run, I ran and catched hold of him; he dropped the bacon; I collared him; there were other people came; I left him to them, and took up my hat and wig, and bacon from the dirt."
The Oxford English Dictionary has an even earlier usage. From a poem by John Skelton, dated to 1523:
To Mistress Isabell Pennell
By Saint Mary, my lady,
Your mammy and your dady
Brought forth a goodly baby
So a writer may have a child character saying Mammy or Daddy at any date from the early sixteenth century.