Can vampires drink blood from kids?
Short answer: yes, but it's not ideal.
Long answer: Kids can't become vampires because they are not strong enough to survive the early stages of the disease, so if a vampire bites a fae child, it's basically a death sentence for that kid.
But when vampires don't want to turn their victims, they just harvest their blood via an incision and bottle it. However, a vampire can't get very much blood from a child without draining them to death, so using them as "bloodbags/cattle" is considered a waste of time.
Sometimes in a desperate situation, the children of heavyweight species are considered (ogres, minotaurs, centaurs, etc.) but they are not convenient because they will only grow bigger and stronger with time. Vampires prefer to keep weaker victims that they can easily overpower, like humans and other fae.
Overall, children just aren't very worthwhile victims for vampires. But that's not to say vampires never prey on them, because they still do from time to time. Kids are much easier to kidnap than adults, so a desperate vampire is more likely snatch one for a quick feed.
A full drink will kill the average child, so when vampires snatch kids, they do it knowing they will have a body to deal with afterwards, and that just makes things more complicated. Dead children get a very strong reaction from the public, and this paints a bigger target on that vampire's back, so it's still not an ideal way to feed. Vampires prefer to draw as little attention to themselves as possible.
I imagine hunting children is a "last resort" situation. Easy prey in a pinch, but too high risk for too little reward.
This subject actually comes up in the story "Eat Your Heart Out". A vampire named Dario ends up with an infant after kidnapping its mother to feed on her. Dario is so disinterested in the baby, viewing it as such a waste of his time, that he doesn't even feed from it. Instead, he sees more value in feeding it to his pigs, which he uses for meat to feed the "bloodbags" in his dungeon. I think this is how most vampires regard mortal children.
There are also more righteous vampires, like Zeffer, who resist their bloodlust and refuse to hunt children out of principle. Sadly vampires like him are far and few between...Vampiric bloodlust slowly corrodes any virtues they had as mortals and claims most of them eventually.
(Hence while vampires are considered "evil" by default. Nobody contracts vampirism thinking "Oh boy, I can't wait to murder children!" but...given enough time, most of them find themselves doing just that. Because they're desperate for blood and it's an easy solution, at least in the moment.)