As Jason points out in his excellent answer, River has a brief opportunity to kill the Doctor in the corn field and does not. She then tries to kill the doctor at the very next opportunity she gets (shortly after she regenerates).
I want to suggest a reason why she didn't kill him at that very first opportunity in the corn field.
River likes to learn about things, after all she became an archaeologist. She has been brainwashed into thinking that the doctor is dangerous and must be killed. It is only natural that she would be curious about this dangerous man and want to learn a little about him before killing him, which she had every reason to believe she could do at any time.
I think her words to Madame Kovarian in The Wedding of River Song give us a hint at why she would be interested in the Doctor.
RIVER: It was such a basic mistake, wasn't it, Madame Kovarian. Take a child, raise her into a perfect psychopath, introduce her to the Doctor. Who else was I going to fall in love with?
chakotaya.net: Doctor Who s06e13 The Wedding of River Song
Obviously, she doesn't fall in love with the Doctor until later, but I think this explains why she was curious about him from the start.