When does Katniss first realize that Peeta does care for her and is trying to keep her alive?

i would say, being an expert, the time with the bread at his parents bakery back in the district when they were eleven.
he seemed to notice that she was gonna die of starvation pretty soon, if not then.
and even though he got a nice shiner (bruise), im sure he knew she would not ever forget that.

if you are talking about the first one.
i don't remember but my guess is either after the tracker jacker incident or when they back at the capitol and watching the games and she sees Peeta take on cato i think it was when the tracker jackers attack.
im pretty sure it was either time.

well in the first book, i think that katniss starts to feel that peeta cares for her when they are in the cave and the announcer announces that some backpacks are going to be out in the cornocopia and peeta is wounded from the leg, katniss tells him that she has to go but peeta doesnt want her to go because she might get injured or even kill:/

when they are in the cave in the hunger games and she is taking care of him

She suspects it when Peeta takes on Cato to save her but blames it on the star-crossed lovers show, then in the cave it hits her again when she's afraid he'll die (twice), when he tells her about when he fell in love with her and she remembers some things as true. When she is in the Capitol and she sees the replay of the Games and when Haymitch says "Don't have to, he's already there" and she thinks "Already desperately in love"... then she really realizes when they're on their way back to 12 and Peeta finds out all she did was 4 the Games