Vlad is a very hard lane for most people, Quinn included. You need to be super aggressive level 1 with passive > E > passive combos to establish a dominant footing. You have an edge in harass during the first stay in lane but around level 7 his Q and E just start trading too well. Your best bet at this point is just to be patient and make sure you stock up on HP pots and rush a vamp scepter into either Botrk or BT. You usually won't win an all-in against him if you are both even in items until late game. It's important to just play the lane safe and wait for jungler help. Try to be on the lookout for when he Q's a minion and immediately go in for a quick E>Passive>Q trade. Back off and force him to Q another minion. If you keep this pattern up you might initially lose out on some CS but it will pay off in the long term by letting you not fall to his harass and opening the door for a potential all-in win against him forcing him to play safer as well.
As for general Quinn playing, I like to play her as an assassin up until mid game but I build like an adc the entire time because I know that is eventually what I will be. Standard IE/PD core is my rush the majority of the time. If the enemy has a few bursty champs that could pose a problem then BT is a viable choice too for the shield so you can still come out on top after 1v1ing them. Constantly be on the lookout for the enemy adc going to farm a minion wave. Immediately pop ult and go chase them down. It's pretty much free kills. Biggest thing to remember though is that late game you don't have an ult. You really have to play like an adc and resist the temptation for tag teaming to close in on someone. Tag team essentially becomes another TF ult late game in that it's only used to clean-up stragglers after a teamfight (or for ganks on isolated targets as mentioned earlier.)
Gl!
