Gosh, well I just came back to look at this. OP I see you say your daughter is autistic. I think the life of a professional musician would be very challenging for someone with those special needs - a musician's life is erratic in hours, locations, and earnings. You need to juggle a lot of different skills and be extremely self-reliant in terms of doing what's needed musically as well as chasing work, running your accounts as a freelance (almost all musicians are) and so on.
Just as an example, let me tell you about my day today. I've just come back from a 3 hour rehearsal; we sight-read our way through a pile of stuff which we're performing on Friday. I had to sit still, listen, count, play, stare into space while others did their bits, and concentrate non-stop. Then I jumped on a train and buzzed home, in time to catch up on a bit of diary management (organising bookings, website, accounts, promotional stuff) and next I've got three hours of teaching. Then as soon as I finish, I grab a bite to eat, and I'm heading out to another rehearsal, this time chamber music preparing for a small concert at a later date, which we are promoting ourselves, so which has no financial guarantees at all attached.
The day is broken up into lots of small but intense bursts of work and involves interacting at a complex level with a lot of people, some of whom I might never have worked with before, or might never again. It is fulfilling and pays OK, but is hard work and requires a lot of flexibility.
None of these things are probably what you envisage for your 4 year old in thinking about a career as a musician, and I doubt they are the kinds of demands that an autistic adult could deal with very easily.
I'm glad you are supporting your child's music, but really - she's FOUR!! Stop worrying about Maxim Vengarov and how old he was when he started. Some musicians start at four, most don't. I personally was 10, and ended up at a London conservatoire and with a good career. You really can afford just to mess around at this stage, be it ballet, brownies, gym, or whatever.