Moore is a non-naturalist cognitivist (it's not just the non-cognitivists like Ayer and Hare who are non-naturalists as Jill Oliphant's textbook suggests), because he believes that goodness can be known - cognitivism, but not by a posteriori sense experience, so non-naturalist. Rather, it is an a priori concept - a non-definable property of an action, like yellow is a non-definable property of a thing. A link is given at the bottom of this extract to the whole of Principia Ethica. these extracts are from chapter 1 (paragraphs in brackets).
Consider yellow, for example. We may try to define it, by describing its physical equivalent; we may state what kind of light-vibrations must stimulate the normal eye, in order that we may perceive it. But a moment's reflection is sufficient to shew that those light-vibrations are not themselves what we mean by yellow. They are not what we perceive. Indeed, we should never have been able to discover their existence, unless we had first been struck by the patent difference of quality between the different colours. The most we can be entitled to say of those vibrations is that they are what corresponds in space to the yellow which we actually perceive. (§ 10 ¶ 2)
Yet a mistake of this simple kind has commonly been made about "good." It may be true that all things which are good are also something else, just as it is true that all things which are yellow produce a certain kind of vibration in the light. And it is a fact, that Ethics aims at discovering what are those other properties belonging to all things which are good. But far too many philosophers have thought that when they named those other properties they were actually defining good; that these properties, in fact, were simply not "other," but absolutely and entirely the same with goodness. This view I propose to call the "naturalistic fallacy" and of it I shall now endeavour to dispose. (§ 10 ¶ 3)
If I were to imagine that when I said "I am pleased," I meant that I was exactly the same thing as "pleased," I should not indeed call that a naturalistic fallacy, although it would be the same fallacy as I have called naturalistic with reference to Ethics. The reason of this is obvious enough. When a man confuses two natural objects with one another, defining the one by the other, if for instance, he confuses himself, who is one natural object, with "pleased" or with "pleasure" which are others, then there is no reason to call the fallacy naturalistic. But if he confuses "good," which is not in the same sense a natural object, with any natural object whatever, then there is a reason for calling that a naturalistic fallacy; its being made with regard to "good" marks it as something quite specific, and this specific mistake deserves a name because it is so common. As for the reasons why good is not to be considered a natural object, they may be reserved for discussion in another place. But, for the present, it is sufficient to notice this: Even if it were a natural object, that would not alter the nature of the fallacy nor diminish its importance one whit. All that I have said about it would remain quite equally true: only the name which I have called it would not be so appropriate as I think it is. And I do not care about the name: what I do care about is the fallacy. It does not matter what we call it, provided we recognise it when we meet with it. It is to be met with in almost every book on Ethics; and yet it is not recognised: and that is why it is necessary to multiply illustrations of it, and convenient to give it a name. It is a very simple fallacy indeed. When we say that an orange is yellow, we do not think our statement binds us to hold that "orange" means nothing else than "yellow," or that nothing can be yellow but an orange. Supposing the orange is also sweet! Does that bind us to say that "sweet" is exactly the same thing as "yellow," that "sweet" must be defined as "yellow"? And supposing it be recognised that "yellow" just means "yellow" and nothing else whatever, does that make it any more difficult to hold that oranges are yellow? Most certainly it does not: on the contrary, it would be absolutely meaningless to say that oranges were yellow unless yellow did in the end mean just "yellow" and nothing else whatever-unless it was absolutely indefinable. We should not get any very clear notion about things, which are yellow-we should not get very far with our science, if we were bound to hold that everything which was yellow, meant exactly the same thing as yellow. We should find we had to hold that an orange was exactly the same thing as a stool, a piece of paper, a lemon, anything you like. We could prove any number of absurdities; but should we be the nearer to the truth? Why, then, should it be different with "good"? Why, if good is good and indefinable, should I be held to deny that pleasure is good? Is there any difficulty in holding both to be true at once? On the contrary, there is no meaning in saying that pleasure is good, unless good is something different from pleasure. It is absolutely useless, so far as Ethics is concerned, to prove, as Mr Spencer tries to do, that increase of pleasure coincides with increase of life, unless good means something different from either life or pleasure. He might just as well try to prove that an orange is yellow by showing that it is always wrapped up in paper. (§ 12 ¶ 1)
My objections to Naturalism are then, in the first place, that it offers no reason at all, far less any valid reason, for any ethical principle whatever; and in this it already fails to satisfy the requirements of Ethics, as a scientific study. But in the second place I contend that, though it gives a reason for no ethical principle, it is the cause of the acceptance of false principles-it deludes the mind into accepting ethical principles, which are false; and in this it is contrary to every aim of Ethics.
For full text of Principia Ethica click on this link: http://fair-use.org/g-e-moore/principia-ethica/s.13