The ending of Breaking Dawn Part 1 explains itself in three steps: Bella survives the birth only because Edward changes her, she wakes as a vampire, and Jacob's bond with Renesmee stops the wolves from harming the baby. Edward injects venom into Bella's heart as her body fails, which is why the film closes on her waking with red eyes as a vampire.
Why does Jacob not kill her? He believes the baby is dead and moves to attack Bella, but the moment he sees Renesmee he bonds with her. In practice, that bond removes the wolf pack's main reason to hunt the family, which sets up the tension in the next film. Away from the Cullens, the Volturi learn about the child and about Bella's change, so the threat now comes from outside Forks.
In my opinion, the film ends where it does because it is only half a story. Part 1 spends nearly all its time on fear, a pregnancy that looks like a death sentence, and then answers it in the last minutes, while the consequences are left for Breaking Dawn Part 2. It could be argued that this makes the finish feel abrupt, but the fear is resolved and the danger is only moved. If you want to see how the books handle the same events, Twilight books vs movies compares the two.
The structure also pays off a promise the saga has been making for three films. In Eclipse, Bella is already asking Edward to turn her, and here the change finally happens, but in the worst possible way: on a delivery table, with Edward driving venom into her heart as a last resort. Compare that with New Moon, where the Volturi were the distant danger in Italy. Here the post credit scene, with the Volturi receiving Carlisle's letter about the wedding and Bella's transformation, brings them to the family's door. Part 2 then opens exactly where this one stops, with Bella waking as a newborn and Irina misreading Renesmee from a distance. One nice irony is that Jacob, the character most hurt by the wedding, is the one whose imprinting protects the family. That reversal is, to me, the smartest piece of plotting in the film, because it turns the pack's threat into a shield without a single line of explanation.