Hi Benas,
I will be in the same boat at the beginning of next year as my wife will deliver while we are still waiting for her approval by Immigration Canada. I looked a bit over the forms to fill for my baby also in order to transfer my Canadian Citizenship to her. And yes I came up with the same question as you. Now thinking logically (that's what I always do at work as I am an engineer
) of course a small baby does not have any picture IDs. Even kids that are not so small usually do not have any picture IDs except maybe a passport. But this does not apply in our case as you are applying for the citizenship (and probably you are applying for a limited validity passport at the same time).
My way of doing this, is not bring any picture IDs, but write a small letter, one paragraph not more stating that this is a baby born abroad and applying for citizenship, no IDs for a one month old. Also, since you have to submit it to the closest Canadian embassy, I suggest submit the application package in person and explain the situation to the embassy personnel. They are responsible for receiving and will be able to help you out if you need something else for a baby since no picture IDs are available.I have been to a Canadian Embassy in the country of my wife and they were actually very nice in explaining me the process to obtain citizenship for my future daughter who is not even born yet. So embassy personnel is a good resource to be 100% sure.
Maybe some other people have had this experience and cane share with us?