Hello there Den,
John has beaten me to it but I'll post just the same.
“Pop” in the context used my your grandmother is probably a non-alcoholic, carbonated, flavoured, and sweetened soft drink usually commercially prepared and sold in bottles or cans. “Sprite”, manufactured by the Coca-Cola Company, and therefore - I imagine - readily available in Australia, is pop. It is not specifically a Birmingham word and in the UK is sold in a number of different flavours: lemon, lime, orange, raspberry, blackcurrant, dandelion and burdock, etc.
If you have read a wide variety of posts on this forum, it is highly likely that you have come across the word “Vimto”, which contains the juice of grapes, raspberries and blackcurrants, flavoured with herbs and spices. It was a very popular “pop” when I was a boy, i.e. 1950 to 1960 and probably well before that and possibly afterwards as well. It is still produced but I can’t comment on its popularity today.
Although a form of “pop”, I have never heard of Coca-Cola being referred to in this way.
Best regards,
db84124