i run a dolphin Hang on back filter with some Sera Siphorax. Nitrate is there simply because the bacteria in the media is doing its work to convert ammonia to nitrates, at the bare minimum, you should have sponge filters.
I had a YT and a pair of clowns in that small QT which means its bioload is very high, coupled with nutritional feeding, its normal for nitrates to sky rocket. But like i mentioned, high nitrates do not generally bother fishes until it exceeds extremely high level ( i would assume above 100ppm).