It could be food allergies. Are there pimples elsewher? Thighs, buttocks, upper armss?
We use Amlactin. It is over the counter lotion. It's not cheap, but it helps. Just be warned, it may burn the first few times you apply it so apply a very thin layer.
I was always told not to use hydrocortizone or any cortizone treatments on young children, especially only 1 yo. Their skin is too thin and it can make their skin even thinner and do permant damage.
The acne may also just be something that you will have to put up with and she will grow out of it as she ages.
If it really bothers you, then I suggest you see a dermatologist.