Dear H.,
This all depends on how well you know your child.
Will she be able to sit still?
Will she be overstimulated by the whole situation?
Is she overly sensitive to sound?
I was raised, fortunately enough, with the privelege of going to the San Francisco symphonies and ballets and operas. As a kid, it was such an awesome place that seemed to command respect...it was kind of like going to church. There was something so soulful about it. I personally think more children should be exposed to those things. Having a bit of refined behavior and sensibility does not ever harm a child. Unless, you know for a fact your kid will be bouncing off the walls and you still take them anyway. That wouldn't be a good experience for anyone. The symphony is not the place to expect a child to behave out of the blue.
I'm not saying that's your case, by any means...but if your child behaves well in other situations, it's something you can talk about regarding how special it is. It's a big building, there will be people playing musical instruments, everyone is on their best behavior.
What I really loved.....everyone got dressed up. I wore my best dress and shoes, slept with pink foam curlers in my hair the night before. It was event.
I don't think 4 is too young chronologically.
Maturity is a different matter and only you know the answer to that.
I think you should take your daughter and also take lots of pictures of your family outside the building and make it a memory.
Please let us know how it goes....