Be careful selling to customers overseas unless you're 100% sure of their safety laws regarding baby items. Australia and New Zealand have similar laws in this regard. If you sell to a country when you don't know their laws you leave yourself vulnerable to law suits.
The quote “a customer is always right” may not be completely accurate but pretty close. Customers are your bread and butter. A happy customer will become an advocate and advertise you for free because they’ll tell all their friends. If a customer has issues, do everything in your power to help them and BE NICE. With social media in play if you get snippy with a customer they will tell everyone online who will listen and it’s so much better to be known as a helpful and lovely business than a nasty one. Your business won’t last if this happens.
Try to never bad mouth other businesses. There is several reasons for this first it's a mean thing to do and second customers won't thank you for it. Some feel they can self promote by putting competitors down, it will actually back fire. Many consumers don't like to deal with nasty nellies and those businesses are just trying to make a living to. BE NICE.
How do you sell? There’s Etsy, Ebay, Facebook, your own website. The first 3 are a good cheap way to begin and get your name into the market. Once you decide to have your own website do a lot of research. There are lots to choose from Wix, Big Commerce, Shopify etc. They vary a lot. Also know that you can buy your own domain such as www.yourbusinessname.com.au and many people make the mistake of purchasing this through the website company they use and it’ll cost quite a bit. You can purchase it separately through a domain registrar. Godaddy is a reasonably priced one. As with an ABN once you buy the domain other companies may contact you to pay the yearly fee for it and may charge $100 a year instead of $15 a year for example. So do your research.
Regardless of how you choose to sell it is a good idea to have a Facebook page as it's a cheap way to get advertising. Get family and friends to share your page and hopefully go viral.