It is recommended nationally that all children aged 6 months to 5 years should take vitamin drops. It's not quite as straightforward as saying breastfed babies/toddlers don't need them, it also depends on the rest of their diet and in relation to vitamin D other factors too. I am not saying that they are essential for all children, but it is worth considering the issue in relation to your personal situation. As a population-wide recommendation it does make sense, as there is good evidence that a sizeable proportion of children in the agegroup covered by the recommendation are not getting enough essential vitamins and minerals.
One study showed that alomst half the children aged 1.5-4.5 years had intakes of vit A below the optimum level, and 38% for vit C. 20% of children in that agegroup had low iron stores.
Gregory JR, Collins DL, Davies PSW, Hughes JM, Clarke PC. 1995. National Diet and Nutrition Survey: Children Aged 11/2 to 41/2 Years. Volume 1: Report of the Diet and Nutrition Survey. London: HMSO.
When thinking about a baby under 12 months it's also worth being aware that other factors influence may influence baby's status. For example, iron status may linked to early cord clamping (which prevents all the baby's cord blood being transferred into the baby), vitamin D status in the baby is linked to how much vitamin D the mother had when pregnant, although during breastfeeding it is the baby's own exposure to sunlight that is more important.
This is a recent thread on vit D, with some handy links.
Personally, I choose not to supplement my dcs, as I am happy with the range of food they consume (which is not necessarily the same as what I offer!) and their exposure to sunlight. Best to make an informed decision though, and not simply to dismiss public health advice as rubbish.