The "mortal peril" clock first appears in Goblet of Fire, a later novel.
Harry Potter and the Chamber of Secrets, first published in July 1998, takes place during Ginny's first year at Hogwarts. Harry Potter and the Goblet of Fire, first published in July 2000, takes place during her third year.
The Weasleys have two unusual clocks. A wall clock in the kitchen informs the family when it's time to do particular tasks:
The clock on the wall opposite him had only one hand and no numbers at all. Written around the edge were things like 'Time to make tea', 'Time to feed the chickens' and 'You're late'.
— Chamber of Secrets (Harry Potter #2), Chapter 3: "The Burrow"
A grandfather clock in the living room — the "mortal peril" clock — shows each family member's location and status:
Mrs Weasley glanced at the grandfather clock in the corner. Harry liked this clock. It was completely useless if you wanted to know the time, but otherwise very informative. It had nine golden hands, and each of them was engraved with one of the Weasley family's names. There were no numerals around the face, but descriptions of where each family member might be. 'Home', 'school' and 'work' were there, but there was also 'lost', 'hospital', 'prison' and, in the position where the number twelve would be on a normal clock, 'mortal peril'.
— Goblet of Fire (Harry Potter #4), Chapter 10: "Mayhem at the Ministry"
We don't know if the Weasleys possessed the grandfather clock during Chamber of Secrets, or if it always worked as a safety monitor. Even if it is a family heirloom, its current configuration (with the hand for Ginny) can be no older than Ginny herself, and it's possible — maybe even likely, given Mrs Weasley's worry for her family(1) — that the Weasleys acquired and/or enchanted it in response to the Chamber incident.
(1) Mrs Weasley's greatest fear, as she admits to Lupin, is that a member of her family will die:
'I see them d– d– dead all the time!' Mrs Weasley moaned into his shoulder. 'All the t– t– time! I d– d– dream about it...'
— Order of the Phoenix (Harry Potter #5), Chapter 9: The Woes of Mrs Weasley