The job market for FNP's in pediatrician's offices varies greatly from city to city. It's really simple matter of supply and demand.
If you live in a city where the local nursing schools
produce a lot of FNP's and PNP's, you may have trouble finding such a job -- particularly right out of school. Such jobs are attractive and there can be lots of competition for them. So, if there is a large supply of FNP's and PNP's in the area, it can be tough. Pediatrician's will be more likely to hire someone with extensive experience as a pediatric nurse than someone right out of school and you may have to wait for your ideal job, and get the needed experience first.
On the other hand, if you live in a city where there is no nursing school
pumping out large numbers of FNP's and PNP's, you will have less competition for the types of job you seek.
You'll need to discuss this with local people "in the know" to get a good picture of your local job market.