grammaticality - what kind of an animal vs. what kind of animal

An excerpt from Java for Dummies, 6th Edition:

If you already know what kind of an animal Java is and know that you want to use Java, skip Chapter 1 and go straight to Chapter 2. Believe me, I won’t mind.

Is it grammatically correct to say what kind of an animal instead of what kind of animal which, as far as I know, should be the only correct way to say it? You see, I always thought that this type of construction was never supposed to be used with articles, even thought I had heard that colloquially English speakers sometimes do say it like that, slipping in an article here and there. And the example that I'm posting here is from a textbook on Java programming. Therefore, you would think that the grammar should really be tip-top, but, as you can see for yourselves, it's obviously not. So, what do you guys make of it? And if there's a method to the madness as to when we use one or the other that you may have heard of, please feel free to share it with me and other English learners.

Let's suppose that the writer had instead written this:

If you already know what kind of animal Java is and know that you want to use Java, skip Chapter 1 and go straight to Chapter 2. Believe me, I won’t mind.

How would the meaning be different?

Answer

Your question:

Is it really grammatically correct to say what kind of an animal instead of what kind of animal...?

Yes, it is. It is possible to keep an, though it's fair that you'd expect it dropped because it's usually dropped. Then again, it's quite obvious that his writing style is informal.

This entry of Practical English Usage by Michael Swan should help explain why both alternatives (with or without a/an) are possible.

551 sort of, kind of and type of

1 articles
The article a/an is usually dropped after sort of, kind of and type of, but structures with articles are possible in an informal style.

​　　That's a funny sort of (a) car.
　　What sort of (a) bird is that?

So, if it were:

If you already know what kind of animal Java is and know that you want to use Java, skip Chapter 1 and go straight to Chapter 2. Believe me, I won’t mind.

would the meaning be different?

Not at all (to put it simply), because in his usage, what kind of animal would mean the same thing as his what kind of an animal.