Judging from their website, Target has cowboy hats in various child and baby sizes.
I am sure they can help you or make one to suit your needs. If all else fails, you could order one on eBay. I just checked, and they have lots of really cute ones for affordable prices.
Shepler's has kids' hats. I don't know if they have a store near you, though. sheplers.com/kids/hats/ Here's a switchboard.Com directory of western-wear shops in Texas (you can narrow down the results if you want, though): tinyurl.com/cvn5pv That's if you want a "real" hat for the kiddo.
If you're just looking for a cheap one for, say, a photo op, you can check the toy department at Walmart. Here's an online source if you don't have any luck in brick-and-mortar stores: smallinthesaddle.com/hats.html.
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