Congratulations on finishing your schooling! How often you work with children in your job as a public health nurse depends on the types of programs your health department offers. For example, in mine, there are more nurses who work with families with children than don't. I work in the clinic setting, so I interact with kids when I give them their vaccinations or do family planning appointments for teens, so I don't work with them very much. But there are home visit programs where you might visit women while they are pregnant and then continue to visit as their newborn grows in order to help them get a grasp of parenting skills for early childhood and connect them to resources. There is another program for children and youth with special needs where nurses act as case managers to help connect the kids and their families to resources and medical clinics. My health department also has a partnership with the county human services office where a nurse visits families that have an abuse or neglect case open with human services to help the family remediate whatever issues led to the case opening in the first place. In some jurisdictions, public health nurses are also school nurses so there is that route also.
If you want to work directly with peds in public health it can certainly be done, although the role is probably closer to home visitor/case manager than direct care like you may find in a private duty nursing gig. You'll still have direct interaction with them, just not as hands-on as acute care. Take a look at your local public health department's website to see what types of programs they offer - if you don't see any that appeal to you, you may need to look at moving to another area that does have those types of services. In the meantime, as a new grad nurse, you can start networking in public health by joining your state's public health association to learn about job opportunities or find a mentor. Find your state's affiliate here: State & Regional Public Health Associations
Good luck, and let us know how the job search goes!