“I understand they want all the data, but we know that the vaccine has been extremely effective at preventing severe disease in all age groups and is very safe,” said Dr. Tress Goodwin, who practices emergency pediatric medicine and is a mother to three-year-old twins in Washington, D.C. “It’s crazy to think that my kids won’t be vaccinated until more than a year and a half after I got vaccinated myself.”

“It has been demoralizing when that goal post keeps getting pushed further and further down the line,” she added.

Cheryl Hillis of High Point, N.C., was so concerned about protecting her 3-year-old daughter that she enrolled her in a Pfizer trial in Atlanta and made the long road trip to that city twice. She will hit the road a third time at the end of the week, for the final dose. Ms. Hillis has been home-schooling her three other children — ages 9, 11 and 14 — until her youngest gets vaccinated.

Like some other parents who answered the newspaper’s callout, she does not expect a pediatric vaccine to protect against infection as well as the adult vaccines did when they were first authorized, before an onslaught of variants cut their potency. At this point, she said, many parents are mainly interested in staving off long Covid, hospitalizations and deaths among the youngest demographic.

“We have almost no options to keep our children safe, save isolation,” she said in an interview.

Pfizer said that its new results showed that three doses, with the third given at least two months after the second, stimulated the immune system to strongly protect against the virus, with no safety concerns. Researchers said the immune response of the subset of trial participants, measured one month after the third dose, compared favorably to that of people 16 to 25 who received two doses. No supporting data was disclosed, nor was the number of children in the subset.

“We are pleased that our formulation for the youngest children, which we carefully selected to be one-tenth of the dose strength for adults, was well tolerated and produced a strong immune response,” Dr. Albert Bourla, Pfizer’s chief executive, said in a statement. Dr. Ugur Sahin, chief executive of BioNTech, said the companies would complete their F.D.A. application for emergency authorization of the pediatric vaccine this week.