In my hometown, most of the immunization takes place in camps in potential social areas where it is convenient for caregivers(eg: schools, nurseries, etc). The most common way is to hire a photographer or incentivise him/her other than money. But myself being a design student I believe there are young photographers who would volunteer or at times it can collaborate with such schools(design, art or photography). Another way can be to invite photographers to conduct a portrait photography workshop. The specifics can be discussed accordingly. This is purely from the context of my hometown Pune, Maharashtra, India; and I will have to work out the same for other demography for other contexts.
One important thing that I wish to be considered is some intervention in the structure of the camps to diffuse maximum sunlight and avoid using artificial light. This is because the photo should preferably be candid to bring it to life in the longer run.

Hello Youngbae Chee
My idea is very much the same as yours. One of the very main difference is that my idea focuses on causing a ripple effect and inspiring communities as in the Indian context the main reason that caregivers immunize their wards is trust that comes mostly because others in the community do the same. In such a scenario the goal becomes easy once the process is initiated. The proposed idea also tries to facilitate this initiation.
It would be helpful if you give it a glance.
https://challenges.openideo.com/challenge/briefsgates-vaccine-innovation/ideas/photograph/comments#c-7d71341ad8c9e8039bfd5915c17b7a4e

Also, I will be happy to work together if possible.

Thanks, Anne-Laure Fayard.