How to counter early dragon attack

For starters Black is playing a Kings Indian Defense, not a dragon.  The Kings Indian Defense, is often a race with White trying to break through on the Queenside, before Black breaks through with his King side attack.  Generally when you play d4 you should not place your knight in front of your c-pawn.  The most common way to play after 1.d4 is 2.c4 staking out a claim in the center and committing to queenside play.  This is all very general and there are different ways of playing d4 opening, but this is the most common and most fundamental.

I agree with blake78613. The Knight should only come to c3 after a space-gaining c4 push.

That's not a KID.

Actually, Black's structure pretty closely resembles a KID, so it seems like that is what he was aiming for.

It also closely resembles a dragon.

The KID and the dragon aren't systems. This is just a sort of modern defense where white didn't play well.

However, that's not the point. OP: If your opponent gives you the center, take it. Don't play e3 if he allows you to play e4. If in the original position the e3-pawn was on e4, white's pieces would have much more freedom and it's much easier to play.

Neither Dragon, nor KID. More like putting out pieces in random.

Bg4 has some meaning if Black adds pressure to d4 by pinning the knight. Obviously not the case here (d4 is securely protected), so why not 5.h3 to force Black call his bluff?

It isn't the orthdox dragon attack, but...does sorta resembeles it's basic idea of that bishop putting pressure right down to knight's pawn. But yeah, I understand it a bit now. This is pretty much an unorthdox attack which capitalizes on opponents mistakes with the initial pawn movement. 

I know I'm not good, I have a lot to learn and I don't think that way either. 

Rather than protecting the d pawn with e3, stronger would have been e4 and Be2 (Pirc/Modern?). Then, if Bxf3, you can recapture with the bishop and your queen still guards the d pawn.  I think that's why you played e3 instead of e4.  Another way to play it would be to play c4 out before Nc3 (King's Indian Defence) which is more aggressive or c3 and Nbd2 (Colle System) if you want a more solid defense.  Otherwise, your opening looks pretty descent.  Just unnecessarily passive is all.

A little historical trivial:  The Dragon variation was named by Fyodor Dus-Chotimirsky who wrote, "I first uttered this name in Kiev, in 1901.  I was an enthusiastic astronomer, and while looking at the sky I noticed how the Dragon constellation resembled the pawn structure...d6,...e7,...f7,...g6,...h7 seen in the Sicilian Defense.  So I decided to call the opening the Dragon Variation."