try adding a little sugar to the veg. Over time take the sugar out. It should condition her to associate the taste of the veg with the sweet reward.
(Also, fresh organic veg tends to have a much higher sugar content. I don't want to make assumptions about your veg source, so I bracket this. But it would be interesting, if only from an experimental POV, to offer store bought vs home grown veg and see what a child reaches for :) )