My name is Ursula, and I am an LPN. I have been a nurse for seven years.
Before nursing school, look for volunteer opportunities with children. Even if it isn't medical, any experience with children will help bulk up your resume.
During nursing school, request peds clinical rotations as much as possible. Also, when you graduate, you may not be able to become a peds clinician initially; however, school nursing is a great means to start working with children, and is much less competitive since the pay is not anywhere near as much as acute care RNs'. I worked as a school nurse for several months and I loved it. I did some browsing on Indeed.com, and it looks like in your area there are lots of agencies looking for LPN and RN peds nurses for home health, which would entail a 1:1 basis of caring for a medically fragile child. Most agencies do not require much experience, so this is another means to bulk up on experience in order to get a hospital job if that is your goal.
Hope this helps =)