Billabong Lucky You babydoll dress. Lucky you in this new favorite little dress from Billabong. Easy babydoll dress in a floaty fit with long blouson sleeves and a tie at the scoopneck. Light and airy woven fabric with an allover print. An icon in the surf industry for decades, Australian brand Billabong got its start when founder Gordon Merchant started producing board shorts by hand in 1973. Now, they maintain a prominent presence among surfers, while also creating swimwear that looks just as good lounging on the beach as it does riding the waves.