Rose undergoes a significant transformation during her time with the Doctor. Initially, she comes across as a very ordinary girl. There isn't much to set her apart from anyone else. She meets the Doctor because she was in the wrong (or right) place at the wrong time. However, the Doctor sees something in her, so he brings her with him on his travels. The first season gives us an opportunity to see what the Doctor saw. She's sweet, fun, and adventurous. Most importantly, in the episode Dalek, we see the depth of Rose's compassion.
In Dalek, the Doctor and Rose meet the last of the Daleks. This Dalek is broken from years of torture. Rose touches the Dalek, unwittingly allowing it to regenerate (but also transferring DNA). The Dalek tries to murder its way out, and nearly succeeds. Rose however, is spared by the Dalek. The Doctor then shows up ready to kill the Dalek, but Rose prevents him. She sees the transformation in the Dalek and pities him. Even though she's seen the Dalek kill hundreds there's no hatred or desire for violence towards the Dalek. If there's an alternative to violence she's all for it.
The end of season one and the Christmas special at the start of season two proves to be a turning point for Rose. For the first time things depended fully on Rose. Only Rose could save the Doctor at the end of season one. And in the Christmas special, only Rose could save humanity, or so it seemed. Rose ends the Time War by pouring the Time Vortex into the head of the Daleks and killing them, saving the Doctor and all of Earth. In the Christmas special, Rose was asked to speak on Earth's behalf. In her own words, she had to be the Doctor. Rose is now a major actor.
As season two progresses Rose becomes more like a partner to the Doctor, and less of a subordinate. She takes matters into her own hands repeatedly. Her compassion also continues to fade. In particular, it's shocking that neither she, nor anyone else are bothered by the horrific death that the Doctor serves up to the Cybermen. Perhaps, though, she's simply caught up in the moment too strongly. However, one would expect some reflection at some point on the tragedy that she has just witnessed. Her compassion is being suppressed, or at least is directed now only towards the helpless. It could be too, that her love for the Doctor has made her willingly blind. She's loyal to the Doctor and her family, almost to a fault.
Her movement towards partner is in a sense completed in the two part episode The Impossible Planet and the Satan Pit. The Satan is trying to escape from prison. Both the Doctor and Rose play equal parts in preventing his escape - Rose by killing the bodily manifestation of Satan. The rest of season two is a telling of their love and a resolution of their partnership, a partnership, as we will see, of the like-minded.
On Wednesday we will develop some of the themes we sketched in this post as well as conjecturing at what happened to Rose while she was away from the Doctor, by looking more in depth at three episodes, The Parting of Ways, Tooth & Claw, and Doomsday.
 We don't see the same compassion towards the Slitheens in the earlier two part episode. However, there was no other option for the Doctor, and it was their death or the death of the entire planet. Perhaps it's better to say that she's vigorously opposed to needless violence.
 More on this scene in Wednesday's post.
 I find that speech in the Christmas special to be the most difficult scene to watch in all of Dr. Who. I feel so bad for the spot she was in, she was so unprepared.
 The Doctor clearly is bothered but doesn't see any alternative.