Bringing food into Australia ca be a BIG problem. Certainly they won't permit anything fresh like fruits or nuts/seeds, they'll be confiscated. Canned goods would be ok to a degree. Australia has very strict bio security laws. With regards to the milk in the carry on bags, normal LAG ( liquids and gels) protocols would apply, so don't go over the limit of 100 millilitres. ( I think 8 oz is over this?).
Without grandstanding, our bio security can seem like a bit of overkill for first time visitors, ( you can get fined smuggling in an apple if you get caught), but its there to protect the wildlife we have here. Australia is an island and our native plants and animals have no protection from a lot of pests and diseases that can be accidentally brought in from food/nuts/seeds that are in most other countries.
In saying that though, I think you'll find our range of produce here is extensive, and you should have no problem purchasing food items to make a meal suitable for the allergies your child has.
Good luck and have a great trip!