I don't really agree with everything in the previous post. A lot of anesthesiologists do some peds, but mostly the straightforward stuff. Most of peds in the real world is pretty routine (but still requires a level of vigilance) as opposed to what is seen at big institutions. General anesthesiologists are adequately trained to handle routine peds. If you do the fellowship you're more likely to work at a bigger place, but it doesn't limit you to a place with a childrens hospital, by any means. If you're interested in academics, then you would be more limited to institutions with dedicated children's ORs.
The trend is to have peds anesthesia done by pediatric anesthesiologists because that is what parents want. So many large groups have slots for peds trained folk. In fact, there is quite a demand for peds. In order to just do peds, you need to have a place that does enough kids to have dedicated ORs just to peds. In many places, cases get moved around depending on what rooms finish first, so peds could be moved in or out of your OR and an everyday anesthesiologist needs to be able to do it.