Katharine McPhee Pregnant, Showing Off Baby Bump with David Foster

Katharine McPhee's letting the cat out of the bag, sort of ... but we've learned what you think is true really is ... because we've learned she's havin' a baby!!!

Sources with direct knowledge tell TMZ ... Katharine is indeed pregnant. She was out on a stroll Tuesday in Montecito with her hubby, David Foster.

They were out getting ready for the new kiddo ... browsing at baby stores. They left The Nurture Cottage with a bag full of items.

David is gettin' up there ... he's 70 and already has 5 grown daughters. It's not unheard of, for sure ... Tony Randall, of course, is the champ having his first 2 kids in his late 70's.  And, of course, Mick Jagger, who has a 3-year-old ... he's currently 77.

The first-time mom had her small dog in a swaddle-like bag over her shoulder.

The news comes just days after Katharine sang "She Used to Be Mine" from the musical, "Waitress." During that performance, Katharine strongly hinted she was pregnant ... cradling her stomach while singing "... and the life that's inside her, growing stronger every day."

Congrats!!!