GPs say they want the programme to get off to a successful start and are committed to carrying out the work, but have voiced concerns over whether they have sufficient resources.
The first phase is being launched next month, with 119,000 two and three-year-olds being called into surgeries to be given the vaccine, administered as a nasal spray. In addition, a pilot scheme is to run this winter in which 100,000 older children in selected primary schools will be offered the vaccine.
Dr Alan McDevitt, chairman of the British Medical Association's Scottish general practitioners committee, said it would put more pressure on surgeries.
He said: "We do have concerns about the resources to deliver the programme in general practice, but have committed [members] to undertake it because we think it is important. The resources to deliver such a large vaccine programme are significant and it will put a strain on general practice, community services and schools.
"However, because it is so important, we are all endeavouring to get it started successfully and would encourage all children and parents to ensure they accept the offer."
It will be the first time all youngsters will have the chance to receive the vaccine. Previously, only those classed as being in one of the at-risk groups -such as young carers or children with conditions such as asthma - were offered the vaccine.
Dr McDevitt added doctors welcomed the programme, which should significantly reduce the number of cases of flu, and save lives. Children were particularly likely to spread the flu virus once they caught it, he said.
Scottish Conservative health spokesman Jackson Carlaw said he also supported the programme, but the Scottish Government needed to plan its implementation carefully. "Each year there are thousands [of people], particularly in the at-risk groups, who are missing out," he said. "That has to change, and it's why any inoculation campaign has to be matched with the right resources. It is too important an issue to get wrong, and I hope the Scottish Government provides the support and resources needed to make this work."
The nasal spray is being used because it provides children with better protection from flu than the previous injectable vaccine.
Parents have also welcomed the development.
But Nicola Lamond, spokeswoman for Netmums, the parenting website, said many parents wanted to know more details about the spray and when their children would get it.
"Overall I do think it's a good idea. Flu can be a nasty illness," she said. "But I would like to hear more, for instance about whether the vaccine has any side-effects and when older children will get it."
The programme will go on to be extended, with children at all primary schools and selected secondaries offered immunisation from next year, and the vaccine being available for all aged two to 17 from 2015. By the end of 2015, some 919,000 in the age group will have the chance to receive it every year.
It is likely that GPs will eventually deliver the vaccine to all children under school-age and older youngsters will receive it at school.
The programme is being rolled out gradually, mainly because it will take time for sufficient numbers of doses to become available.
It is being brought in following advice from the Joint Committee on Vaccination and Immunisation - a body advising health departments in the UK.
Scotland's chief medical officer Sir Harry Burns said earlier: "The vaccine offers excellent protection against those types of flu virus that are most likely to be circulating each winter, protecting your child from a nasty illness that could end up with them having treatment in hospital."
A spokeswoman for the Royal College of Nursing Scotland said the detail of who would be administering the programme still had to be finalised in discussions with the Scottish Government and health service.
A Scottish Government spokesman said: "We note the concerns of the BMA, but they have agreed to administer the flu vaccine for two and three-year-olds this winter. The vast majority of the programme will not be administered by GP surgeries, but through schools by NHS boards."