If you can control your priming and resulting carb pressure you can bottle it any way you want. Just know that quad takes more sugar and time due to it's very heavy final gravity. If you use the same amount of prime sugar as regular beer you should be fine in normal bottles, slightly undercarbed. If your recipe includes any extra carbing provisions, you may need more than regular bottles for protection.
I found it took quad a long time to build any pressure at all- 6-8 months in one batch which I primed "normally". In my opinion quad needs extra priming to reach full carbonation. Doing this may require heavy duty bottles .
I have bottled quad in the belgian style brown swing tops 500 ml. I believe they are made for wheat beer as that is traditionally highly carbonated. They are expensive but a great presentation for your long awaited prize brew. You wont be disappointed. Any premium brew of mine finds it's way into some of those. I also use the poly 500 ml bottles. They may split ( e.g. older ones ) but won't blow up like a bottle bomb with high pressure. I've had only one so far make a mess in the storage room.
Personally I now keg mine and bottle about 6 - 500 ml poly bottles per batch with double the normal amount of priming sugar, one rounded teaspoon per 500 ml. As long as you have surely come down to final gravity, you won't have overpressure.
Poly bottles allow you to gauge pressure by squeezing them. Slight hardness is good-getting there, rock hard is over pressured. Over pressure can be fixed with a quick twist of the cap over the sink.
I find with keg carbing the quad takes wayyyyy longer than most other brews as well. Ah, a fresh batch of quad- lucky you- have fun and enjoy! CHEERS!