Why does this person not try to kill the Doctor at the field?

Question

In the Doctor Who episode "Lets kill Hitler", If

Mel was raised and trained by the Silence to kill the Doctor,

why don't they kill the Doctor the first time they met him in the field ?

Even after crashing into Hitler's office, they only try to kill him after getting shot and

regenerates into River song.

To me it almost seemed that it wasn't their intention to kill the Doctor (based on their behavior) and only after their change did they suddenly get a brainwave that "Hey its my mission to kill the Doctor, lets get started on it now"

Answer 1

She answers this rather flippantly in the episode itself:

Doctor: If you were in a hurry, you could've killed me in the cornfield.

River: We'd only just met. I'm a psychopath. I'm not rude.

^{Doctor Who Series 6 Episode 8: "Let's Kill Hitler"}

So her capricious nature has to count for something at this point. However, I might more reasonably point out that she also doesn't really have a lot of a chance to kill him:

• In the corn field, she's trying to resolve the immediate problem of being chased by the police
• Once in the TARDIS, it doesn't make an abundance of sense to kill the only person who can fly it
• Once arriving in Germany, she has to contend with the noxious smoke pouring out of the TARDIS, and the Doctor (almost immediately) stealing her gun
• And then she meets (and is shot by) Hitler
• Once she regenerates, we have to make a certain allowance for capriciousness again, but also her trying to reformulate the plan; since, apparently, she knew that the Doctor knew that she was there to kill him, she needed some time to prepare

Once she made the (admittedly, probably not terribly wise) decision to not just shoot him in the cornfield, she didn't really have a lot of time to kill him.

Answer 2

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.