Hmm, that's a good question. I suppose it would depend both on where you go to school and how your local hospitals operate. For example, I work in a major children's hospital in the Peds Critical Care unit. My hospital does not employ NP's, nor are they allowed "privileges" in the PICU. If the NP is the primary doctor for one of our patients, they are allowed to be updated on the plan of care and the patient's conditions, but they cannot write orders or direct the plan of care. Those decisions are made by our intensivists (attending MD's).
Similar is true for our acute care pediatrics floor, although practitioners from other services (such as oncology practitioners, surgery, GI, pulmonology, etc) are allowed to write orders for the patients and some of those services do employ NPs. But we don't have any NP's that are employed specifically to manage the patients on the floor.
I think the best thing you can do is try to find out if there are NP's that work in peds acute/critical care in your local hospitals. If there are NP's, see if you can get in touch with them and ask how they came to be at their current job.
Perosnally, I would never want to be an NP in peds critical care. The kids are very, very sick and a lot of responsibility and a huge amount of knowledge/experience is required to effectively manage their care. I much prefer being the RN at the bedside, performing assessments and nursing skills, getting a through understanding of the patient's baseline, and catching and reporting changes. Yes, there are times when I have to quickly identify that something is wrong and take steps myself to intervene and correct the problem.
I'd really urge you to spend a few years in pediatrics or pediatric critical care before you peruse a degree as an NP with the intention of going into one of those areas.
Best of luck!