Going by the PHB, elves hit the Venerable category at 350 years old, and have a maximum age of 350 + 4d100 years. So yes, she could have been in a battle 300 years ago - she'd be about the human equivalent of being in her late 60s now, and she was probably inexperienced at the time of the battle (or is/was some kind of prodigy). Likewise, she could have been in the battle 700 years ago; she would be the equivalent of a human that's just over 100 years old now, and she would have been a child/adolescent when that battle took place.
Then again, being an elf she probably isn't showing her age in the slightest. She's got all the standard age penalties and bonuses, but they're all under the surface.
Which is interesting, if you think about it. For elves having one of their own die of old age and not look any different physically than the rest of them. No stooped frame and wrinkled skin... your old friend Bill(thiel) looked exactly like you've always remembered him. It's just that one evening he went off to reverie and somewhere in the middle of it all his body went totally limp... and like just llike that, he was dead.