Can a one year old girl get their period?

No. If you have an otherwise healthy child who is bleeding from the vagina, she has almost certainly been sexually molested. You need to have her seen by a doctor and initiate a police investigation for two reasons: 1 - the perpetrator needs to be stopped, because molesters repeat their crimes; 2 - if it comes out later and you haven't reported it, you could be held liable for child neglect or even accused of it yourself.