It's a poor queen move. I suggest you try the Berlin variaition where the knight develops there early.
Ruy Lopez: Smith Defence

You shouldn't worry too much about the doubled pawns resulting from the Spanish Exchange since there is compensation on the black side (easier piece development, bishop pair). Like what Chess4001 is saying, moving the queen so early just to keep the pawns from doubling in this situation seems unwarranted.

Sorry Michael, you're 166 years too late. Bernhard Horwitz played this against Staunton all the way back in 1846

Arctor, yeah, I saw some games. Horwitz blundered a lot in one game.
But still I think quite equal position?
IM pfren, it has a name? Frankfurt variation? Oh, I didn't know that...

So you saw that it was first played over 150 years ago and still didn't think it naive to name it after yourself?
1846?? The copyright's expired. All bets are off. Frankfurt has to take Smith to court. There, they can argue about who gets a bad opening named after themselves.
LOL. MSC, no one really plays this horrible move and there is a reason why it is original. There are just better moves that develop other pieces rather than the queen.

Here is the bust of the Classical Ruy with 4...Qf6, by my good friend GM Kotronias:
I cannot find any improvement on Black's play- white's initiative is crushing. 11.b4! simply kills Black. The idea of the move is 11...Bxb4 12.Ng3 Qg4 13.h3, when the g3 knight is not hanging (as it would be with a bishop on c5). So, Black's queen has to retreat to e6 or d7, but after 14.Nh5! the position is just horrible for Black.
Why not 19...Rd7? Inaccuracy?
However, I must agree black's position is quite "crushed".
Just for that, I'm not even gonna' play 4...Qf6! That'll fix ya'!
lol! nice stuborness!

3...Qf6 has little independent value. The most consistent reply for White is 4. c3 when Black's best reply is 4..Bc5 transposing to a variation of the Classical Defense.
MSC, you have weak argument points for your so called "Smith Defense." There is a reason why your "novelty" is original and extremely rare. Play it and let some players exploit your silly queen move. You should not develop your queen so early!

Thanks for the info, pfren. I noticed you judiciously ignored my suggestion of throwing Qf6 into the Cordel gambit. It looks good for about two seconds, but then reality sets in. After getting crushed in about a half dozen blitz games, I think I might have to give up the ghost. There are no words to describe how bad 5...Qf6 is, so here's an illustration:
11.Qb3 is as bad as 3.Qf6
Isn't 11.Re1 slightly better?!
True, not very usual 3rd move. I guess you don't see it very often.

1. e4 e5
2. Nf3 Nc6
3. Bb5 Qf6
I chose C60/01 or C60/01a for ECO.
Because it has no name, I decide to give it one. Before than, I played Ruy Lopez 3.a6 but I didn't like doubled pawns. I avoided it with queen although it's not good to bring your queen out early.
I tried some variations later. I saw that the main problem is to develop the knight.
Exchange variation, with trap for beginners:
C60/01 Ruy Lopez: Smith defence
C60/02 Ruy Lopez: Smith defence, exchanged variation
What do you mean, your opinion? Suggestions?
Comments desired & appreciated!
M. Smith