Has she tried the list of things posters generally recommend for migraine?
You can get v hung up on finding a food trigger but many people don't have one and it just creates an obsession keeping a diary.
Migraine likes:
Regular hours - bed same time, getting up same time, good amounts of sleep
Not getting hungry - making sure you have a healthy diet, don't skip breakfast, don't go from sugary snack to sugary snack. Lots of us have found quitting sugar/going low carb really helps as you have levelled out your insulin and you aren't getting the peaks and troughs
Being really hydrated - especially if your daughter is prone to low blood pressure this is really important. Water bottle at all time, drink masses
Not having a low blood pressure - salt is good! If your daughter tends to have a low blood pressure generally then upping salt content of her diet will help a lot and stave off dizzy spells which link to migraine
Screens - use the blue light filter on everything, install apps like f.lux if they don't already have a filter.
Stress is often a trigger but avoiding stress is the world's least helpful advice - plus lots of migraineurs then get them when they relax after stress as well. Everyone gets stress in their life, just people born with migraine, tend to do migraines with it 
Personally I would say that if she only has migraine every few months, a preventative is too much and a beta-blocker is not a great choice if she has low blood pressure anyway.
This really helpful article (warning - it is all in medic speak) summarizes the current state of the evidence for treatment.
www.bmj.com/content/bmj/360/bmj.k179.full.pdf
It suggests she should be having intranasal sumatriptan to treat acute attacks and the best evidence for a preventer is pizotifen.
However the good news is that the majority of people grow out of it 