It is NOT safe at all.
There is almost no information about how it will effect kids. We know more about the safety of heroin and crack cocaine in kids than we do about melatonin (I'm completely serious). And if the melatonin was bought in The US then you have no significant guarantee of the purity and dosage of the drug. In the US "supplements" like melatonin don't have to be tested or approved so it is not a pharmaceutical grade substance.
Also melatonin has been shown to NOT be effective in treating insomnia or jet lag. You may have think it helped you but a large number of major studies show that melatonin is no more effective than placebo. Even for melatonin to theoretically work it would have to be given at a very specific time that could only be reliably determined by a doctor talking with you.
A prescription drug called Nuvigil (armodafinil), a non-amphetamine stimulant is the only drug that has significant evidence that it works. It almost became FDA approved for Jet Lag but it needed more study.
If her jet lag is really bad take her to a doctor, don't just give pills to her.
I am a medical student (M.D., C.M.) at a university in Montréal, QC, Canada for psychiatry and internal medicine. I have a Hons. BSc in pharmacology and I have interned with two psychiatrists and one neurologist. I have also worked as a pharmacy assistant.