Did her father die before the queen was crowned?

I'm guessing that "her" here refers to either Elizabeth I or Elizabeth II. The answer in both cases is "yes".

It would be unusual for someone to be crowned while that person's father was still alive, though it could happen. For instance, if Elizabeth II were to die today, Charles would become King despite his father Prince Philip still being alive, because Philip isn't King, he's just married to the Queen. Philip is a descendant of Queen Victoria and therefore IS in the line of succession to the British throne, but he's pretty far down it (around 1700, I think).