The PCs are testing the rumor—so make a choice!
Your campaign is a custom one, so while purify food and drink maybe should apply only to food and drink that's consumable by a creature of the race casting the spell or by the god that grants the spell or something, that doesn't mean the campaign's pixies aren't actually food for everybody.
In other words, the PCs have heard rumors of a creature that gains power via snacking on pixies, so when the PCs cast purify food and drink on a pixie corpse and they or their goat friend is about to dig in, you've to decide if those rumors of greatness through faerie feasting are true. (Fun Fact: PCs—and players!—will likely be disappointed if such rumors are untrue.)
If the rumors aren't true, the spell simply fails. No harm, no foul, no pixie picnic, no übergoat. All done.
If the rumors are true, then you've to decide how true. Can anyone partake of this pixie power-up? Need the pixie be alive? (Ew.) Some degree of fresh? (A day sounds good.) Must the entire pixie be consumed? ("Pixie wings taste like fruit roll-ups!") Is that healthy? (Likely not.) Must pixie be prepared a certain way? ("It must be served... on a stick!") Do a certain number need to be consumed to gain ultimate pixie power? And so on. Then the spell works, but, maybe, after consuming the pixie, the PCs are left wondering why their goat has a bellyache instead of awesome pixie powers.
This is your campaign, and—to challenge the frame a bit—this is less about how the spell purify food and drink works and more about the effects of pixie-eating in your campaign. That is, determine event's outcome and steps required to reach it first, and the question about the spell likely answers itself.
Clever, but not likely.
Purify Food and Drink states:
All nonmagical food and drink within a 5-foot-radius sphere centered on a point of your choice within range is purified and rendered free of poison and disease.
Mileage may vary with DMs, but whether or not the brine pool that the elder lives in would be considered Drink is suspect. It also requires that it be entirely contained within a 5' radius sphere and there are no dimensions for that brine pool.
How big is the pool?
But given the following description of the Brine Pool (MM, 221), it seems unlikely that it is such a small pool.
Most illithids belong to a colony of sibling mind flayers devoted to an elder brain- a massive brain-like being that resides in a briny pool near the center of a mind flayer community.
It is very unlikely that this "Ultimate expression of Illithid domination"(Volos, 173) is forced to live in a 5' radius pool at the center of the community - and anything larger than 10' won't be able to be purified.
Potability
Nowhere in the description of the Brine does it say it is poisonous or filled with disease - just that it is foul and brackish. That doesn't mean you can't drink it, and without it stating Poisonous or Diseased, Purify Food and Water wouldn't affect or change it.
But a DM could rule otherwise, but probably shouldn't.
If it was 5' radius pool AND your DM considered the water in that Drink (that is also currently poisonous or diseased) for a PC, then it may be possible to do this. But it's very much a DM dependent design and decision, but the above information does suggest that the pool is too large and without language on the Brine being Poisonous or Diseased, there just isn't enough to allow this against such a powerful and legendary creature.
In support of alternate rulings, see the Water Weird (with a caveat)
The Water Weird (MM, 299) has the following property that isn't in it's stat block but is in the description:
A water weird loses its evil alignment if its waters are cleansed with a purify food and drink spell.
This does imply that Purify Food and Drink does do more than the spell description alone - however, this is also a case of specific beats general. The general rules of Purify Food and Drink have strict limitations (and no upcast options to expand them) - but the Water Weird has a specific reaction to the casting of the spell. A DM may choose to allow a similar reaction by the Elder Brain, but this is purely in homerule territory and all should be aware of the difference in effect (an alignment change for a CR 3 monster vs an end-state for a CR 14).
Best Answer
The description of the effects of a black dragon on the area specifies
Not all water is fouled, just the sources of water. Therefore drinkable water can certainly exist in the radius of a black dragon. In the absence of a rule specifying otherwise, purify food and drink should work as normal and purify any water it is cast on.