Here are a few things to consider. Most will depend upon how interested your daughter is in playing softball. MYGS does provide bats and batting helmets to each team.
At minimum you will need the fielding mask and a fielding glove.
Fielding face mask: MYGS does require / recommend all kids in the Rookie and Minor divisions to wear an infield mask (pictured below). Each team will have one or two to use however we do not have enough for every team. It can either be the hard plastic or metal. Cost approximately $35-$40. This is a great investment, not only for your kids safety but it will also make yourself and your daughter more comfortable playing catch in the yard.
Fielding Glove: Range in size from 9.5” to 11.5” for kids in the rookie division. Its best to try on and see what fits your daughters hand.
Softball bat (for Fastpitch): If you think she will continue to play, you might want to consider getting her a bat. In the rookie age group, it should generally be 26” 27” 28” in the rookie division. No need to buy an expensive bat, as by the time your daughter moves up to the minor division (3rd, 4th, 5th grade) you will mostly likely need a new bat that is between 29” -31” depending upon her size. It’s nice for kids to have their own bat/equipment. It seems to get them more interested in it and you can practice in your yard or playground more. There is a video on what bat size to purchase. Rule of thumb is to measure from the center of chest to the tips of her fingers with her arm stretched out. https://www.baseballmonkey.com/learn/baseball-bat-buying-guide#measuring
Softballs: Rookie league plays with a 10” soft ball. Its softer when you squeeze it than a normal softball. Buy one or two to play catch at home or practice hitting between practices and games.
Batting Helmet: Batting helmet with mask (mask is required on helmet). Approximately $20-$40. With COVID, a lot of families decided to purchase their own helmet this past year so they wouldn’t be sharing helmets.
Extras: (If you daughter is super interested in playing, I would add the following):
Hope this helps, if you have any other questions feel free to contact me.