Since you say she has a lot of the classics, I won’t suggest “Goodnight, Moon” or “Babar” or “Where the Wild Things Are” or the ever well loved “Pat the Bunny.” Since she has Mo Willems, it sounds as if she enjoys books with a sense of humor– Click, Clack Moo– Cows That Type by Deborah Cronin would fit the bill and is a Caldecott winner (as was one of Mo Willems’ books).

I’m partial to anything by Kevin Henkes; you can’t go incorrect with him or David McPhail. For Henkes, you might try Kitten’s First Full Moon, about a kitten who thinks the moon is a huge bowl of milk. It’s done in black and white, kid friendly and also won a Caldecott. (I’m also partial to Bailey goes camping, but last time I checked it was out of print.)

I’d also recommend any of the Max and Ruby books by Rosemary Wells. In fact, I reckon the last books I bought as baby gifts were the Max and Ruby board books, so they could be used early and often. Max and Ruby are bunnies; Ruby is the huge sister and always bossing Max around, so of course Max gets the best of her.

Shirley Hughes’ Alfie books are also very excellent– I like Alfie Gets In First, in which Alfie gets locked inside the house while Mum and Annie Rose are outside.

The Olivia books by Ian Falconer are fun, too.

All of these are picture books, by the way.

But if you want something really new, I’d go to http://www.powells.com/subsection/NewArrivalsChildrensPictureBooks.html

which is Powell’s Books listing of new children’s books. You can read a bit about them too. I see that Rosemary Wells andMarc Brown (Arthur) have teamed up for a new book called “The Gulps” and David McPhail has a new book out called Water Boy.

Excellent luck!

Two relatively new baby boy books that I LIKE are
Hush Small Alien
Huge Box of Boynton: Barnyard Dance! Pajama Time! Oh My Oh My Oh Dinosaurs!