She can do it in First Aid, but one thing to think about is where First Aid is compared to where she will be eating and the time from when she does the injection to when she eats.
If it’s a full service restaurant, she may not get seated or served right away. Even with buffets, guests can get food right away, but may have a wait time between checking in and getting seated.
Counter service restaurants may have a fairly long wait time to order, depending on how busy it is. You want to look into WDW’s remote ordering option where guests can order ahead of time and pick up their order with a minimal wait.