well I think you would pot then sigil? But don't see the point. Pots have short cooldowns and somehow I doubt that Queen can go through 3k hp every 8 seconds or whatever the cooldown is.
If you pot 1st, QoT will run away with mana, which means she will come back at you soon enough after priest heal and army rebuild.
If you sigil, you will make her sigil, then you large pot, and she is in danager of going to 1HP 1st, and /or run out of mana, which is death. This will kick her out of the lane back to base.
Also, the large pot may work once with QoT. Try it again and you'll have an interrupt waiting for you, and then you are in trouble if this was your "not die" strategy.
This is not to say the good QoT isn't dangerous, but against the best DGs when they are fresh, you are going to lose.
Consider these scenarios when you are exposed and not tower hugging (like pushing a flag or defending a portal 1vs1)
eg: UB + Spit / Ooze + BotS + Health Stack. This guy is going to have 7K life and you are going to have 4.5K or 5K depending on item choice (or no mana which is worse). You cannot win if you are both fresh and have sigils. If you are not fresh you are going to die unless a double tower is real close. If he is not fresh he is going to get away, he just has to TP and you can't stop him.
Tower Rook with Boulder 1+ & Hammer 3+. QoT cannot escape the boulder stun / Hammer combo at a certain distance because she it too big of a foot print. You are going to die fighting this against a good player as your only defense is to not fight. Basically, if you can spike, you are too close in an internet game. If he queues a step back, steps forward, and you lag, you are dead as you will move forward into the death zone. If you don't target him, you aren't going to hit him in his towers.
Assasin Oak. This is just all around bad for you. He is going to put a beat on you so badly you are going to want to cry. Snare/Interrupt/AoE Boost/Life Stack... Pen will interrupt a Ground Spike if you do it right. Everything you do he does better. He will beat you by 25% life everytime if you don't run. If you don't run early, you aren't going to get away. If you run early, you're the one who needs to go to base, not him.
Sedna: You cannot kill her... eventually you cannnot hurt her and will run out of mana in a battle. A level 20 QoT has no chance against a level 15 Sedna simply because she can regen faster than you can do damage. I've tried, you are going to need to leave the engagment every single time.
LE: It's LE... do we really need to go there?
That leaves Reg, TB, and Da...