I wouldn’t recommend carbonated drinks until primary school age, actually. And only if your little one can brush her teeth very well. The carbon dioxide and sugar are lethal to the teeth. Kids can get severe tooth decay. As for ice cream, I offered my daughter a bit since about close to 2 years old? But we brush her teeth very well 😁 And she’s underweight, so we allowed her some sugar.
For me, I will set a example for her to follow. If I don’t allow her to eat , I also won’t eat. Or you can eat when you all are not together.