Turkey is renown for all the "bamboo" and other exotic child/baby friendly clothing materials in the market. There are alot of popular baby brands that make their products there. Lots of local stock too.
In all honesty, buying solely online is never the best idea - but if you must - you could go to "trendyol.com" or "hepsiburada" switch it to translate to English and it'll give you some good ideas. The currency conversion is 12 TL = $1 AUD - so it's usually quite lucractive. But you MUST ship in bulk - as shipping can be quite pricey from anywhere BUT china.
I would highly recommend booking your next holiday there, and taking the time to find a textile broker. If you are still interested i have a few phone numbers. The textile broker agents basically put you in touch with all the factories and manufacturers you need to get your product into the market.
If you want to design your own clothing and have it made, that's also quite possible. Turkey's MOQ is much more "forgiving" than other countries. I believe in t-shirts it's like 10pcs. So if you wanted custom baby clothing I can't see it being more than 50pcs.
In fact, finding good children's clothing is very difficult. My sister usually buys clothes for her child on Amazon, there are a lot of stylish things. But recently, they went to a wedding and my nephew needed to find a cool costume for the kids. She stumbled upon the site gentleman's guru, where she found a very cool baby costume. This suit fits her son perfectly. He looked simply luxurious in it; I would like to buy something like that for my son.