The most common and most likely answer to this crossword clue is the 8 plus 5 letter word WHOOPING COUGH
I've seen this crossword clue in Financial Times
W
H
O
O
P
I
N
G
C
O
U
G
H
Buddy explains!
The straight part
We know that "Potentially dangerous baby’s rattle" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case potentially dangerous baby’s rattle = whooping cough.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does WHOOPING COUGH mean?
WHOOPING COUGH noun- A contagious disease of the respiratory system that usually affects children caused by the bacterium Bordetella pertussis, the advanced stage of which is characterised by spasms of coughing followed by a whooping sound during the intake of breath.