>There is nothing dangerous in homeopathy

Some of the pills are made using toxic fillers. It's not enough I'd panic over, you can get the placebo effect without ingesting anything shady/expensive.

Do you have a source for homeopathy being made from toxic filers?

I’d hypothesize that the more expensive the pill, the better the effect.

I can't find specifics about homeopathic fillers, but any pill not regulated by the FDA is likely to use cheap fillers that are often toxic. Vitamins are where you commonly hear about this, see https://en.wikipedia.org/wiki/Regulation_of_food_and_dietary...

I did find this, https://arstechnica.com/science/2016/10/fda-homeopathic-teet... which shows there is some risk, though again you're most likely fine.

>I’d hypothesize that the more expensive the pill, the better the effect.

For you, sure. For your daughter, I bet your confident recommendation is the most important aspect.