The most common and most likely answer to this crossword clue is the 19 letter word STRAIGHTFORWARDNESS
I've seen this crossword clue in The Times
S
T
R
A
I
G
H
T
F
O
R
W
A
R
D
N
E
S
S
Buddy explains!
The straight part
We know that "quality of child’s play" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quality of child’s play = straightforwardness.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.