Larry Flanagan, general secretary of the Educational Institute of Scotland (EIS), called for a "quicker decision" to be made on the roll-out.
He argued offering vaccinations to younger children was a "safer route than just allowing for herd immunity to develop".
The Joint Committee on Vaccination and Immunisation (JCVI) currently recommends only those over 12 are offered a jag.
However, the US has started to offer vaccinations to younger children, and experts such as Professor Devi Sridhar, one of Nicola Sturgeon' s pandemic advisers, have backed such a move.
Mr Flanagan said the EIS would have prioritised school staff for vaccinations and would have "moved much quicker" on 16 and 17-year-olds.
He said this would have led to "less disruption".
Mr Flanagan added: "I hope they make a quicker decision around five to 11-year-olds because I think vaccination should be offered there, to the families of those young people."
He continued: "We are in favour of young people being offered that vaccine and we've said so at SERG [Scottish Education Recovery Group].
"I was surprised to discover at SERG that apparently there is no licensed vaccine for that age group in the UK at the moment, although clearly the USA have started vaccinating that particular group.
"So hopefully there is some work going on to make sure that if a decision is taken to allow that age group to be vaccinated, there will be a licensed product available to them.
"Ultimately we think offering the vaccination is a quicker and safer route than just allowing for herd immunity to develop over a longer period of time, because that would be more disruptive to school education."
Mr Flanagan said the EIS "absolutely accepts there should be informed decisions".
He said it would be for young people and their families to decide if they want to take up the offer of a vaccine if it is made available.
Margaret Wilson, chair of the National Parent Forum of Scotland, said "it will be down to personal choice".
Elsewhere, Mr Flanagan said he would like to see face coverings remain in place in schools throughout the winter.
He also backed rules preventing parents from attending their child's nativity or Christmas concert in person.
The union leader insisted the general guidance "is about minimising the amount of adult mixing there is in the school environment", adding: "The reason that guidance is there is to try and keep schools open, because if we have outbreaks among staff, schools will have to close because of the staffing shortage."
He continued: "Why would you potentially run an event that is going to increase infection level in your school community, particularly in the run-up period to Christmas?
"Because it could then impact upon family celebrations over the Christmas period, when there are alternatives in place."
First Minister Nicola Sturgeon previously insisted her Government was not trying to "stop children having fun".
She said: “We take advice from our education advisory sub-group so that we are basing these decisions on the best available information, and I hope children like the rest of us will have a much, much more normal Christmas than was the case last year."