The Little Concierge Company My Baba 27 March, 2012 Living, Travel The Little Concierge Company is a premium service delivering baby essentials to destinations all over the world. These guys are a godsend, taking the stress out of travelling so you can enjoy your holiday without worrying about packing for your baby before hand, or shopping for essentials once you get there. You can choose the same superior quality products online and choose your delivery address. They also take care of Mum & Dad, offering a large selection of essentials and luxuries. So simple!