I think you will find people weather busy or crowded will be themselves, if they are going to be rude and impatient it will not matter if it is busy and crowded, if they are going to be patient and helpful it will not matter if it is busy and crowded or empty. I have been going to the parks for more than 16 years, visually impaired, crowded and not busy,I have had good and bad experiences in both. With a child I would hope most people would be kind and helpful.
Two things, when I was younger I always felt more comfortable being able to hear my mother, if your child is like that but does not like to stand out, my mother would put bells on her purse so that I could hear even if she got out of my sight. Also, I know by 10 I would not do this, but by then I was blind for 6 years so maybe your child would not mind and find it more comforting, I would ask, those elastic pull cords that you can hook on a toddlers wrist and your own, my mom used it in crowds when I was younger, but as I say by 10 I would not but another child may still find it comfortable.
As for a GAC, you can get one for shows, but for rides the cane works and you will not need a card, when there is an alternative it is usually less crowded and easier on her.
I hope she has a wonderful time, my last suggestion is to do things real early in the day and real late at night, spend the afternoon when real crowded back at the hotel, swimming.