If there any access to lab equipment at all at the school? I’d be surprised (and intensely disappointed, honestly) if a middle school science lab didn’t have at least one spectrophotometerlying around. These are easy to use and could help for this project. See if one is available for final measurements, either at your daughter’s school or perhaps at a local college or university.
Without having done a bunch of background research, if I wanted to begin to design a method for determining the concentration of vanillin in an extract from vanilla beans, I would begin with:
Soaking the vanilla beans in a solution of alcohol. Lab-grade ethanol, methanol and isopropanol would probably be good starting places. Ideally, you’d get something as pure as possible, so no “denatured” ethanol. Vodka is pretty pure water and ethanol, but has other stuff in it which might affect the results.
I’d filter the solution that I’ve obtained, to removed any solids that might be floating around in there. At home, a coffee filter would be a good start. There are better filters available for lab work.
I’d then try and quantify the amount of vanillin in the solution. Vanillin absorbs UV light at 308nm (note: that NF monograph is for vanillin powder, redissolved into solution), so taking measurements at that wavelength in a spectrophotometer would be a good first start. Use filtered vodka as a blank to get a baseline and compare to the solution you make. You might want to consider comparing to a store-bought solution of vanilla extract as well, but that might not be all that useful. If you can get a spectrophotometer that is able to scan a range of wavelengths, you can see if you actually are measuring a peak at 308nm. You might have to dilute your solution a few times to get it down to a level you can measure…you’d have to correct for that to figure out your final concentration.
One thing to worry about is what other compounds you are extracting with your solvent. Vanilla beans are made up of a lot of stuff, and some of that most likely is also going to come out of your beans. If your solutions are brown, then you know they are more than just vanillin+vodka, because vanillin isn’t coloured in the visible spectrum (it’s white as a powder, and is colourless and clear in solution). This basic method will not isolate the vanillin or remove the other components, and so your results will be affected by them.
If you have a super-friendly chemistry prof at a local college or university and if you’re allowed (by the rules of the science project) to go all-out, ask about using an HPLC. In the lab, that would be a method I’d go with 
Thinking about this too much… I believe it’s possible to buy nearly pure vanillin powder or solutions from food companies. Look into it - that can be your standard to compare what you make at home to.
If you can get your hands on a blacklight, you might be able to take things a step further with some sort of chromatography technique. You could, perhaps, get a qualitative measure of how much vanillin you have, or at least of how much other stuff you have, if you run something like a TLCon a coffee filter (I’ve done it with Sharpie marker colours, but never with vanillin!). I can go into further details if you want - I really don’t know if this would work. It won’t help you solve the concentration, but it could help to show whether you have any vanillin at all.
…I no longer work as a chemist, but the basics are fun to explore 