I don't think White has anything better, but Black may be able to mate more quickly with 4...Qg4.
The threat is 5...N(any)+ followed by 6...Qf3#.
If 5.Ne2, Qf3 6.Be4 Nxe4+ 7.Nxd4 Qg2#.
5.Rf1 runs into 5...Qf3 6.Be4 Nxe4+ 7.Rf2 Bxf2#.
Unless I've missed something, black can't delay mate for longer than that - move 7.
Here is a mate in 9 from a recent game of mine. Can anyone spot a mistake? I told my opponent that I thought I had a mate in 8 after making the first move and he resigned, so I didn't get a chance to confirm it. Can anyone find a better move for white on the 6th move?