C.K.
Yes. First of all...I would not recommend Barbizon. From what I have heard they are a modeling school who are only interested in taking your money and getting your child excited about something that may never happen.
If you are serious...and I mean serious. The first place you should begin is JC Penney or Neiman Marcus. Find out if they need any children for catalogs or fashion shows. I have 3 friends whose children model for JC Penney. This is a good start, to see if your child really enjoys it and to give them some exposure and experience.
Next step is go to Kim Dawson or Peggy Taylor Agency. Both do talent and modeling, although Kim Dawson has more experience in Modeling. They will set you up with a photographer for a photo shoot because you'll need to begin your child's portfolio. Note that this can get expensive. But, if you're serious about it, it's an investment. Kim Dawson also has modeling and talent classes.