I would just use another 10. In a true QT the more water the better because there is no live rock. You are mainly relying on a some seeded media to convert the cycle. The more water you have the better to buffer. You'll still likely need to do water changes daily and siphon out waste and excess food to keep ammonia down even in a 10 gallon.
Most sterile QTs are setup with a HOB filter, seeded media (multiples so they can be added/swapped) and PVC to hide and maybe a small powerhead and a heater. The other option is a QT tank which is more of an observation tank that you would not want to medicate a fish in and you should not reuse the LR in your DT. This would require a separate hospital tank if the fish needed to be dosed with something.
Most sterile QTs are setup with a HOB filter, seeded media (multiples so they can be added/swapped) and PVC to hide and maybe a small powerhead and a heater. The other option is a QT tank which is more of an observation tank that you would not want to medicate a fish in and you should not reuse the LR in your DT. This would require a separate hospital tank if the fish needed to be dosed with something.
