As for a liquid equivalent of feed, English doesn't have one. To water is the conventional equivalent. You can water any animal in the sense of giving them water to drink. Indeed, to feed and water is a fixed conjoined verb phrase.
To water in this sense is a straighforward Provisional Verbing, where the subject provides the direct object with the verb's noun. In this case it's water; but other fluids present problems.
Milk, for instance, being a liquid produced by animals, already has a Privative Verbing
- to milk a cow/goat/laugh/sucker
In this sense, the subject deprives the direct object of the verb's noun (milk, or its metaphoric analogs in milking a laugh or milking a sucker), by removing it; the Privative is the opposite of the Provisional. So that conflicts with a Provisional use.
It is possible in some cases to use the same verbed noun in both senses, as in seed a pepper (remove seeds) vs seed a lawn (add seeds); context distinguishes nicely here, because both are conventional activities.
Nevertheless, to milk won't work provisionally; I doubt anybody would understand a request to milk the baby as anything but a private joke. And providing non-humans with milk is not a conventional enough cultural activity to rate its own idiom.