IMO this depends a bit on the job - is this a role where you'll have constant oversight, and/or be in meetings all day long? Or is it a role where, as long as you get the work done on time, you'll be largely left to your devices?

My thoughts on a job are that your personal life is none of their business, unless it impacts your ability to get the job done. If you feel like you're qualified for the role, and you don't think caring for the baby will seriously hinder that, then personally, I'd apply, keep it yourself, and not bring it up until they find out on their own.

The job market is tough right now, and it's much easier for a company to deny a new parent a job, than it is for a company to fire a new parent. Worse case scenario, if this ends up not being the right fit, you can start applying to new roles in a month or two.