Kids have been going through the same trials adulds have and the "effective dosage" about to be approved for kids under 12 is 1/3 of adults, and so far all indications show this dosage to be very safe at these levels. Right now over 96% of doctors have the vaccine. The few medical professionals I know personally that don't I would not have trusted to treat me before the pandemic. I think we'll see similar percentage of these same medical professionals children getting the vaccine. We already know that similar mRNA vaccines have been used for certain cancers (in small trials), including children, that started over a decade ago, with no indcated long-term side effects.
My wife is currently treating more patients with covid at her hospital right now since this started, and her hospital has one of the top infectious disease wards in the country, and received the highest # of covid patients when the pandemic started. She currently has the largest caseload of people under 30 (she does not see childen). She's had multiple young patient get Covid related blood clots which have caused strokes. This is a common phenomenon, but one that has not seen many headlines, although there is clear data on it with a quick search online.
For me, again, it isn't just about death of kids, which is of course a scary proposition. So far, the death rate in kids is very low (indirect deaths from Covid due to stroke, etc. often aren't attributed as Covid deaths, which lead to undercounting the death rate too), but all of the potential side effects, which a vaccine can attenuate, will be the main reason my kids will get vaccinated.
Kids under 12 are also approximately 22% of our population, and are germ factories. If we want to get to an effective level of vaccinated for herd immunity, it is going to have to include vaccine availability to our entire population.
With anything medical related, if you have doubts, look at what the majority of the medical community is doing to help guide your decision.