I've done both and, for a one-day tour, I'd recommend a drive towards Flamingo. You may find that the stop at the Ahienga Trail will be enough wildlife to be memorable.

If you're visiting Florida during the summer, do NOT go all the way to Flamingo -- the mosquitoes are ferocious at that time and place.

If you're going in the winter, the best day to go is when the air is cold and the sun is out. Alligators crawl out of the shade onto the walkways in order to warm up.
www.flickr.com/photos/pr77x/5334450282/in/set-72157625646138065/lightbox/
Just make certain your child RESPECTS all animals enough to get neither terrified of them nor too close to them.

I'd go for Shark Valley.

Another vote for Shark Valley. I've been to both. Our son (8 yrs. old at the time) loved the Shark Valley tour. We have taken twice since then.

Absolutely Flamingo - If you even get that far. Pack a lunch as there isn't any food in the park (a convenience store at Flamingo)
Stop at the ranger station at the entrance to the park and sign up for the junior ranger program. You'll get a book with some activities you can do along the way. (Help if need be to finish up) Turn it back in on the way out for a little hoopla.
There are boat trips out of Flamingo. I like to start there and work my way back -- but leave some time for Anhigha Trail. Or just do anhinga trail. You'll find the "mother load" of gators at the end of the boardwalk.
Did I mention Robert is Here - you won't miss it. Stop there for fresh fruit and milk shakes.
There is an airboat ride by RIH - www.everglades.com

I think Shark valley will be the better choice.
You will enjoy there and also your baby.

Thanks! Is the rest of the park different from the Ahienga Trail? If we go to Flamingo are the other stops different and worth visiting? I'd really like to see the Ahienga Trail and Shark Valley but I'm not sure we'll have time for both.