I can't tell you what the reputable agencies are in St. Louis as I live in KC and my daughter (now almost 4) modeled in Houston, but I can tell you what it was like and how I got her started.
When she was a baby everyone insisted she should be a baby model. I took snap shots and mailed them to about five (5) different agencies in the Houston area. I received a call from Barbazon. They wanted her to model for Foleys (now Macy's). We showed up at about 8:30 one more in downtown Houston, TX and we sat and waited in a small room for about 45 minutes (torture with a 9-month old) and then they called us back. They had clothes picked that they they thought would fit her. They gave me a number of minutes to get her totally dressed (shoes that didn't fit, hat, dress, bloomers) and put her out in front of the camera. She had about 30 shots taken and then it was back into the dressing room to do it all over again.
It was pretty stressful on her and the other kids that were there. I'm not saying I wouldn't have done it again if we still lived in Houston, but I would have been more knowledgable about what to expect and wouldn't have tried to rush her (and myself) so much.
She did make $65/hour. It's based on the age of the baby. Older kids make more, but the market in St. Louis may be a little lower than in Houston because Houston is so much larger. Don't know about that.
Oh, btw, when we moved to KC, the same agency that she had modeled for told me that in KC they don't accept kids under the age of 4 so that could be an issue for you too. Good luck!