Yes, she's right - current advice is that breastfed babies can have vitamin D supplements after 6 mths. Reason is that modern lifestyles may mean the baby doesn't get out of doors often enough to make his own vitamin D.
You can be sure that if you are white-skinned, and you get outside for even a short time with your baby on most days of the week, you will enable him (and you) to make his own.
If you are black or Asian, you would need to get outside rather more, and most of the concern with vitamin D is for Asian and black babies, as they need more sunshine than our pathetic climate proides
Vitamin D supplements are already in formula milk.
It's not that breastmilk is 'short' of Vit D, but our lives these days may be.
In Norway, where all babies are breastfed and it's dark a lot of the year, all babies and children get Vit D supps.
You might find the supplement is packaged with A as well - no real need for A, though.
If you feel you and your baby are out and about enough, then you won't need the supps.
Your HV should have explained all this, but most don't seem to understand it.