Thanks for your consult at DoctorSpring.com.
Menarche is characterized by irregular menstrual bleeding, the same as menopause! Cycles would be irregular, with no definite pattern. It all streamlines within 3 - 6 months at the most, because the hormonal axis is stabilizing still. This is just her first period, and it is very common to see adolescent girls plagued with mid cycle spotting, menorrhagia ( increased menstrual bleeding ) etc.
Factor V Leiden mutation would not cause this generally. She needs to see a doctor only if she is bleeding profusely, and continuously, requiring treatment. Generally, if the periods are very irregular, oral contraceptive pills are prescribed for 3 - 6 months, those are contraindicated in girls with Factor V Leiden mutation.
Right now, please maintain a menstrual diary. In a couple of cycles, this bleeding should fall into a pattern. If it does not / heavy bleeding continues, see a gynecologist.
She can try taking Tranexamic acid - mefenamic acid combinations for the severe bleeding, in case it occurs. At present, since it is not heavy, just wait and watch.
To answer your question - yes, around menarche, such breakthrough bleeding and irregular cycles are very common. Do not worry.
Please feel free to discuss further.