"People" will Google "babylist". Remember that the vast majority of the people using the web have no idea what a browser is, much less a URL. Even when they have a URL, that ubiquitous google box is the place it gets put.

...and google "babylist" returns surprise surprise babylist.co.uk

It seems silly to try and compete with established players.

1. there's caution, and then there's 'thinking small'

2. the owner of the domain is a single-location brick and mortar retailer, with no e-commerce. that would inform my thought process, were in in the OP's shoes

People will go to google and type babylist. (Or even search for babylist.com.)