Thanks for your feedback.... my circumstances are similar to yours - so looks like i may not be in a good position (unless of course EK rules are different from OW rules... but prima facie... they are not...)
The thing is there are no OneWorld rules when it comes to children. Essentially you are reliant on member airlines having their own child policy, that they apply equally to OneWorld airlines, or alternately turning a blind eye. Don't think there is a definative answer.
Interestingly the same trip I mentioned above, on return before the Qantas flight we went to the CX lounge in BKK and had no issues getting in. Anecdotal evidence suggests CX doesn't count small children as guests, but by the same token there is nothing formally written anywhere either to say this, nor say what the age cut-off may be.
So like many things lounge related, unless you are easily offended by the word NO, it cannot hurt but to try.