Pawn and Two: In the 3rd round at Hamburg 1885, Minckwitz played this same variation against W. Paulsen, W Paulsen vs J Minckwitz, 1885. Paulsen played the correct 11.Qd3, with the game ending in a draw.
In "Three Hundred Chess Games", Tarrasch tells of his preparations for his 10th round game with Minckwitz. During lunch, Zukertort recommended to Tarrasch the move 11.Qd2. Tarrasch said he then did no additional analysis, and when given the opportunity against Minckwitz, he played the move 11.Qd2.
Fritz confirms that Tarrasch should not have accepted advice without doing some analysis. The game was about even after: (.13) (21 ply) 11.Qd3 Bb7 12.0-0-0.
Or, if Minckwitz continued as he did against W. Paulsen, 11.Qd3 dxe5 12.fxe4 Qxe4+ 13.Qxe4 Nxe4, then (1.25) (22 ply) 14.0-0-0! as played by Paulsen, or (1.04) (22 ply) 14.Bc6, are very strong continuations for White.
It seems to me Tarrasch should have had lunch with W. Paulsen, not Zukertort!
After 11.Qd2, Fritz indicates that either 11...d4 or 11...Rb8, will give Black some advantage.
After 11.Qd2 d4 12.0-0-0 h6, White should not have played 13.h4?. Tarrasch made no note of this serious error, indicating only that 12...h6 wins the game.
Instead of 13.h4?, Tarrasch should have tried: (-.46) (21 ply) 13.Bxf6! gxf6 14.a3 Bxc3 15.bxc3 Be6 16.Bc6 Rb8 17.cxd4 cxd4 18.Qxd4 Qxa3+ 19.Kd2, (-.55) (20 ply) 19...Rg8, or (-.53) (20 ply) 19...Kg7, with some chances for a draw.