In AmE, if you want another word to refer to a child farting, then you could use toot or poot .
I could not quickly find a reputable dictionary entry for this particular usage of toot , but it is simply an extension of its dictionary meaning (OALD): toot
A short, sharp sound made by a horn, trumpet, or similar instrument.
There is an entry for poot in the OALD US informal Break wind.
‘somebody just pooted’ There are two from Wiktionary: toot , poot
For context, there are many euphemisms for fart .
"Breaking wind" as used above is one.
Another is passing gas (TFD): pass gas Euph.
to release intestinal gas through the anus.
Someone on the bus had passed gas.
It smelled awful.
Something I ate at lunch made me pass gas all afternoon.
This can apply to any person.
Finally, the formal word is flatulence (M-W): flatus expelled through the anus
ell.stackexchange.com/users/36187/Em.
In England a trump is wind that comes out of an arse (and has been for decades to my own personal knowledge so has not arisen from recent world events).
ell.stackexchange.com/users/62201/Dave the Sax
My favourite is from Blackadder: NURSIE: ...and letting off such great and fruit-some flappy woof-woofs!
One can scarcely...one can't believe one's tiny nosy! -- Blackadder 2
- "Beer" Although, this is not a commonly used phrase, except by fans of Blackadder.
ell.stackexchange.com/users/18020/Majenko
You could consider the verb to parp ( Collins ).
Its original and standard meaning is "a honking sound", like the sound made by an old rubber car or bicycle horn.
The word is onomatopoeic (it sounds like what it describes).
But in the right context people will recognise that you are talking about the sound the baby made, or indeed the entire farting behaviour in which the baby engaged.
The word itself is not considered impolite, although the topic still might not be considered tasteful in all forms of company.
I believe it would also be acceptable to use the noun a parp although you might not find that in frequent use.
ell.stackexchange.com/users/8409/joeytwiddle
My child's nursery (in London) called them "windypops".
We still use it.
I'm not sure how common it is, but I think in context
it's fairly obvious to a native speaker.
ell.stackexchange.com/users/64788/Marianne013
My mother used 'blowing off' as a euphemism for fart.
ell.stackexchange.com/users/20194/Bohemian
In our family, they were called a 'scuse', because we had to say 'excuse me' after doing one (as young children, not as babies).
Dictionary.com records 'scuse' as a general abbreviation for 'excuse', but I cannot find any reference to 'a scuse' anywhere on the internet (so far).
ell.stackexchange.com/users/6938/Sydney
What is the appropriate word for "to fart" regarding babies?  As "to fart" is declared as  impolite  in the most dictionaries there needs to be another word for it regarding babies? Like "pupsen" vs. "furzen" in German.
"to fart" in child language
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<word-choice>
ell.stackexchange.com/questions/146732
ell.stackexchange.com/users/64727/Min-Soo Pipefeet
Parp may be a polite alternative to fart, although it may not be frequently used. You could consider the verb  to parp
You could consider the verb  to parp . In the right context people will recognise that you are talking about the sound the baby made, or indeed the entire farting behaviour in which the baby engaged. The word itself is not considered impolite, although the topic still might not be considered tasteful in all forms of company. It would also be acceptable to use the noun  a parp although you might not find that in frequent use.