Yes, you are good for transplant. About size of containers: are you growing autos or photos? If auto, I would go with a 5gal as the final container. If photo you can go in a smaller like 3gal and see how they progress in size and shape, decide the final height and transplant again later on the way with a 5, 7 or 15gal.
Whatever photo or auto or the container, just make sure to bury some of the stem in their new home: put soil up to the cotylodon and remove them. Also they are ready for some wind stress, remove the dome and set an oscillating fan, maybe you will need a humidifier, you can also raise humidity by hanging some wet towels in your tent and have your exhaust fan on a timer.
It is also time to choose witch medium to use because what you have at the moment is a mix of hydro: 20% perlite, 20% coco, 20% clay pebbles, (20% other?) means your medium is at least 60% hydro and 20 or 40% soil, witch is a highway for nutrient, ph, and watering schedule issues. At this point you could go with coco perlite or soil.