Interesting thread. It is difficult to suggest a gift for an unknown recipient, but I'll give it a go.
I'd do something modest but thoughtful for the Vday and 8mos. gift/s. Flowers are always nice and the 'receiving flowers at work/school' idea, never gets old. A nice mix with a few roses and some decent fillers like Callas or white lisianthus, in a tasteful vase that she can hang on to as a keepsake when the flowers eventually fade. Avoid carnations and baby's breath (cliche and very 80's - Trust me, I'm a florist). Order by Monday at the latest if you want them for Vday.
I'd go bigger on the b-day as that is her own 'special' day from everyone else. A pendant as Roland suggested is a great idea. Perhaps arrange for something in the stone of the month you got together (8 months... June = Pearl?) as well as her birthstone and your birthstone. Could be done with earrings instead. White gold seems to be way more popular lately than the yellow golds... just a tip.
Whatever you do decide, make sure it is thoughtful and unique to her taste and style without going way overboard as gift giving occasions early in the relationship will set a precedence for all future occasions....No pressure eh!