Trinity Liliana Coward was found with serious head injuries after the mantlepiece of the stone and marble surround fell on her at her house in Theobald Road, Norwich, on July 6.
The two-year-old was taken to the Norfolk and Norwich Hospital but died shortly after arrival.
An inquest in Norwich heard her father, Shaun Coward, had glued the fireplace to the wall.
Experts said this would not be strong enough to hold the installation.
Dean King, a Norfolk County Council trading standards officer, said that about one child each year dies in the UK in a similar way.
He said: “The incidents all involve surrounds made from stone which are fixed to a wall with an adhesive.” Such projects should be undertaken by a specialist stonemason.
The inquest heard the family bought the fireplace for between £100 (€125) and £200 from eBay about two years ago. Because it was secondhand it did not come with fitting instructions.
Mr Coward bought industrial-strength No More Nails-type glue from DIY store B&Q and fitted it to the wall with the help of his father-in-law, he said in a statement.
Coroner Jacqueline Lake concluded that Trinity suffered an accidental death.
“I make no criticism of Mr Coward — he was trying to make his home look nice and was unaware of the dangers he was facing.”
In his statement, Mr Coward said his daughter’s death had left him “absolutely devastated”.
“She was my rock, she was a real daddy’s girl. I wish I could have died so that she could have lived,” he said.