Yes, you're absolutely right. "Quarantine" means to house the new bird in a separate cage and separate room for a period to prevent the spread of illness that the new bird could be carrying. It doesn't have to be two months, the minimum amount of time should be around 40-45 days
If you get two birds from the same place less than two weeks apart, then yes, it's alright to put them in the same cage. However, after that period, it's quite possible that even the place you obtained the first bird from could have new birds that are carrying an illness, that is why quarantine is so important.
In centimetres, the minimum cage size for two budgies is 75 x 45 x 45 cm
However, if you can afford something larger, bigger is always better!