Life changing event for pets is a worrying time (4,2,7)

I believe the answer is:

rite of passage

I'm a little stuck... Click here to teach me more about this clue!

'life changing event' is the definition.
I can't tell whether this defines the answer.

'for pets is a worrying time' is the wordplay.
'worrying' indicates an anagram.
'time' becomes 'age' (an age is a period of time).
'for'+'pets'+'is'+'a'='forpetsisa'
'forpetsisa' with letters rearranged gives 'riteofpass'.
'riteofpass'+'age'='RITE OF PASSAGE'

Can you help me to learn more?

(Other definitions for rite of passage that I've seen before include "Formative experience" , "Ceremony marking stage of life" , "Very important life event" , "Ceremony marking a change of status" , "Significant event during a transitional period in life" .)

I've seen this clue in The Sunday Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.