The perfect opening?

Before 6.Bf4? I think the opening was fine.

is this any better?

d3 is bad in this situation. it is passive and does nothing to develop your position. if anything all it does is makes it harder to get your rooks active. d4 is much better. also i wouldn't expect your opponent to make symmetrical moves for so long.

I'm not a very good chess player so take this for what it is worth, which may not be very much, but as soon as I saw the black knight come out to f3 I think as white I may have tried moving my pawn on H2 to H3 to try to control the g4 square.  As white, I don't like allowing black to sit on that square.  I also like opening the kingside knight up to e2 instead of f3 so the two knights are supporting one another. Also, I don't like the b2 pawn being unprotected. Maybe move it to b3.?  Having a rook and queen in the same file is usually a good thing but the other rook is not in a file that will be easily open to allow him to have any room to roam.  Maybe but the rook that is on d1 either on a1 or a2 and then push the associated pawn up the board to open the file.  I would think, as black, I would try harder to develop a difference between our situations in my opening rather than trying to match your opening move for move as in the example you have given here.  For my third move, my move would probably be either d6 or G6.  I could be entirely wrong at my level, but as black, this example here  would be a lot closer to the line I would probably try.

The opening primarily revolves around fighting for control of the center.  To that end, it's important to get your pieces out.  But when you play passive moves like 5. d3, you give the opponent a chance to take control of the game.  He might try 5. ... Na5 to trade off your Bishop (giving him the two Bishops) and then ...d5 to break open the center (to open lines for his Bishops).  Then he'd be in control.