The most common and most likely answer to this crossword clue is the 9 letter word PLAYHOUSE
I've seen this crossword clue in Financial Times
P
L
A
Y
H
O
U
S
E
Buddy explains!
The straight part
We know that "What little girls may do in their home/theatre?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what little girls may do in their home/theatre? = playhouse.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 PLAYHOUSE mean?
PLAYHOUSE noun- A child's toy domestic dwelling, either for dolls or large enough for the child to enter.
- A venue for performing plays.