You could do it either way. I worked in adult ICU for years and years before I started doing PICU. However, most of the nurses that I worked with in the PICU started out at other units at the Childrens' hospital.....infectious disease, hem/onc, ER, NICU, burn, pulmonary, neurosurg....even inpatient rehab. We also had our share of new grads that went through the hospital's NA program where they worked in the PICU as NAs part time before becoming RNs where they were able to learn quite a bit about critical care that they would never normally learn in school. I was in the minority starting out with adult critical care. I don't think it makes a difference as to were you start as long as you are intelligent, willing to learn, and love what you are doing.
The biggest challenge I had was getting used to everything done by weight....and that kids compensate very well before they crash vs adults will usually look like hell long before their moment of glory. It didn't long me long though. Now getting used to NICU is another story.....
PICU was my favorite kind of nursing that I did...hands down. I especially liked the great variety that you see in the PICU that you don't see in other kinds of nursing. You can take care of a burn one day and bad wheezer the next and then help admit the open heart the third. It keeps you on your toes and it keeps the mind sharp because technology is always changing, there are always new things to learn and something you've never seen. Its also much less physically demanding than adult ICU as the size of the patients are much more manageable (in general of course). I ruined my knee in adult ICU...and even after replacement it will never quite be the same.
Critical care can be learned. I've seen it. Peds can be learned. I did it. What can not be learned is inborn talent and passion...that you must possess inside of you.
Either route can send you on the path in which you desire.
Best to you in your career,