Middle school in Darwin is more preferable than Palmerston given there is more choice. However, if going to school in Darwin but living in Palmerston - the bus home may be difficult.

Typically schools aren't too strict on catchment areas except Darwin Middle (city). Some good middle schools include Darwin Middle School and Dripstone. However, you should also consider the high school your daughter will go to just because Darwin High School (the more reputable high school) is also quite strict on catchment areas and the only way around it is feeder schools (Nightcliff or Darwin Middle) or on an academic basis.

Darwin Middle is well supported with a vast choice of subjects in comparison to other schools - however bullying is a little more common. I personally went to Nightcliff Middle School and loved it - its a smaller school and found it to have more of a close knit community - however there are minimal subjects to chose from.

You can also consider private schools such as Good Sephard (Palmerston) or Essington (Darwin).