First off I think it's terrific you're interested in this. In my opinion it's the pinnacle of anesthesiology practice. People take various routes. In the past there weren't pediatric cardiac anesthesia fellowships; so most of the senior people in the field are either pediatric anesthesia trained, cardiac anesthesia trained, and/or pediatric ICU and anesthesia trained, who then continued to gain experience by doing cases.
I did a mid-career peds anesthesia fellowship at a large volume congenital heart center and was asked to stay on as pedi-cardiac faculty, basically continuing on the job training. Like a lot of things, people talk about the importance of extra fellowships until they want a body. It wasn't for me, but I say this to illustrate that this is one very common route. As I looked for pediatric jobs, many groups were looking for people to do hearts--and would train you up on the job. IF I were going to do complex pedi hearts, I'd choose to do a year-long fellowship in pedi-cardiac after pediatric anesthesia, if I could at all afford it--six months additional as a minimum. Most people don't go this route, but I've talked to a lot of people and it takes a good long while to get experienced enough so you are not regularly scared doing these cases. For my peace of mind and my patient's health, I'd want a well-supervised training period--more than I got in basic peds anesthesia fellowship, which was a whole lot of pump cases. We ran two rooms a day multiple cases. Finally, I'll say again I'm delighted to hear you are interested in this. What an amazing field--and I sit here rather envious.