Finally got my son's child passport 11 weeks after lodgment. Trying to contact the passport office was a nightmare - it took countless tries just to get in the call waiting queue (all other calls just had a message telling me to call back again before disconnecting, although they make you trawl through 2 minutes of recorded c**p before politely getting rid of you). Then first time on hold got disconnected after 45 minutes. Another half a dozen tries to get back into the queue and then a further hour and a half on hold before call answered.
Fortunately we didn't have a pressing travel date, but I wanted to make sure there was no problem with the application because if we had to start a new one we would be struggling with future travel. All fine as it turned out, just very slow (apparently there are extra steps in assessing child applications)
I did also get a response after a couple of days when lodging a status request on the website which might help others.
There should be an easier way to track the status and escalate delayed processing.