New Line in the Pirc

I call this the Pirc Defence, Taipei Attack.

There's no positions with it in 365chess database, as you can see.

https://www.365chess.com/opening.php?m=7&n=75&ms=Nc3.Nf6.e4.d6.d4.g6&ns=65.124.9.125.70.75

There's also the Accelerated Taipei Attack.

At first glance, this move goes against basic opening principles by bringing out the queen early. However, White's position works quite well as the queen is secure on d3 and cannot easily be attacked. It also controls many vital central squares, as well as further protecting the critical e4 pawn. But White's queen is also versatile, and it could easily move to either the kingside and the queenside if necessary, or even to d3 if this subtle manoeuvre is needed. White is ready to prepare an attack on any part of the board, without creating any weaknesses, and can push for a permanent advantage.

White is at an approximate +0.53 score for the Taipei Attack (at depth 10), so this is definitely playable, and I'm not sure why this hasn't been thought of before (or it has but I just haven't seen it). This definitely doesn't make the Pirc "busted" though as Black can counter the Taipei with a variety of moves, from the obvious (and probably best) 4 ...Bg7 to the odd 4 ...a6. I might do some analysis on these variations, but in the meantime, this is all I got for you guys.

Apologies if you find any flaws in my analysis as I am not a particularly good chess player.

Yes, this variation is ok.  The most known case of an early Qd3 is probably the Alapin's Dutch:

You need to include some actual analysis (at least some sample lines) in the standard g6, 0-0 setup by black to show how you want to develop further since there are a variety of options.

The 3. ... e5 lines don't look too promising:

It's a line.

Against the Accelerated Taipei, Black's most accurate answer might be to transpose into the Hanham Philidor, where Qd3 is just a loss of tempo.

Wht's the purpose of Qd3?

If white aims at fast queenside castling, the stock Be3(g5) + Qd2 setup is much more reasonable.

The purpose is a mere provocation: the White Queen   advances toward the frontline and shows her beautiful chest and other parts of her body!

Ah shoot I meant e3. Sorry about that

3. ...e5 is the main reason why I would honestly play Qd3 a move later, but the loss of tempo isn't too bad for white, as after Nxe5 White's threatening Nxf7+ and then Bd3 gains a tempo on the knight. The point is that Black's never going to play ...e5 this soon in a regular Pirc, but giving the extra tempo makes it playable for both Black and White, and may bring you into weird opening territory that your opponent hasn't prepared.

It might not be the absolute best choice at the highest level of play. However, if it's playable at depth 10, then I would think it's playable at like, say 1600-1700 rating, or at least a rating where thinking up to depth 10 or so is OK.

I also haven't seen it, but yes it is always a possibility that it's been a rejected idea.

About d2 being a better place, you can have your opinion about that, and for all I know you may be right. However, the philosophy of this opening isn't to form a battery with Be3 and Qd2, it's to control central squares with Qd3, and only play Qe3 if absolutely necessary. I've found that Be2 is a decent place for the bishop anyways.

Also note that I prefer the Taipei over Accel. Taipei

Thanks for the advice. Besides, I did a test (which is probably also inaccurate) where I "played" a game with the highest level computer by repeatedly pressing "Switch Sides", basically meaning the computer plays itself. I did this 100 times, all with the same position: Accelerated Taipei (which I thought of first before realizing that a delayed Qd3 is better.) White won 19/100 games, drew 76/100 games, and lost 5/100 games. Again, I'm not sure if this is an accurate test, but I figure it at least proves that it's not 100% busted.

What would you recommend to see if this is a playable opening or not?

Something like that, I assume it would easily throw Black completely off guard. I realize now that the purpose of the Accelerated Taipei is to offer a tempo to Black in return for an advantageous exchange of queens, or have Black risk White having a strong queen that's hard to attack occupying the center. The purpose of the regular Taipei is just to smash Black with an early attack, possibly early queenside castling (though this is not forced!) and dominate the center. It's a little ambitious, but it might work as a surprise weapon to catch your opponent off guard!

White aims to control the center with his queen first rather than to directly attack the kingside right away. I agree, Qd2 seems like a good idea as well, but I would honestly just use this as a surprise weapon once in a while.