I just played against her as Vayne and got absolutely STOMPED lol. How do you counter her in lane as an adc that doesn't have a very good early game? She carried all the way and I was pretty sad. Any advice on taking her on?

you don't beat her in lane, you survive lane and focus on keeping your CS up, hopefully you have a strong defensive support and you outscale her late game, realistically she's supposed to beat you in lane so the only way you're going to win that matchup is either if you have a much better support for the matchup than she does or if you are a substantially better player than them

Or you get a few kills off early ganks.

you either hope for these things:
-MF is horribly worse than you at this game
-Their support is horrible at this game and will feed you kills
-Their jungle is horrible and will feed you kills + buffs (yay)
-your support + jungler are pro and carry your lane

-try to not feed till mid-lategame.

Your jungler ganks, you get atleast 1 or 2 kills early game and your set. Technically Vayne is the worst "early" game adc, as long as you dont feed and get decent cs you should destroy her late game..

I just hate how strong she is. I feel as if double up does too much damage and strut makes it hard to chase her down as Vayne...

Mf is made to win her lane. She is quite the bully. You just survive the lane, cs well and hopefully find the right opportunity to get a few kills in lane from jungle ganks and such.

her base stats (lots o health early) and abilities are mainly used for lane dominance.