There is a scene near the start of the film where multiple people are shot and killed. There is a dog in this scene that the killers acknowledge, but they allow the dog to run away without any harm coming to it. This is the only dog featured in the film.
The MC does get sick at one point after ingesting water from the hatch she cuts at the top of the storage container. It is not explicitly shown in any detail.
Not excessive, no, though there are a few brutal scenes. The most brutal scenes involve someone being shot in the head, and the MC cutting open her leg and then stitching up the wound.
There is a significant scene where the MC is fully naked, her breasts visible, while giving birth. The baby is also naked, though the genitalia is not shown.
The MC is seen presumably defecating into a tupperware container. There are also several shots of soiled baby "diapers" (cloth rags), and of particles floating off of these diapers when they are thrown into the water.
The MC accidentally cuts a ragged gash across her leg on a sharp piece of metal, and stitches this wound herself. Her hands are also injured while cutting open the container.
There are multiple points where the MC is knocked unconscious. First from hitting her head when the storage container falls into the sea. Later passing out while giving herself stitches. And near the end of the film when she's reached her limit, she passes out and nearly drowns.
The MC's hands are injured cutting open a hole in the shipping container. There is no strong focus on the injuries, other than some blood being shown, and cloth wrapped around her hands.
Multiple characters are shot and killed, one of which is shot in the head, and the blood and injury are shown. The MC also receives a giant gash along her thigh from a ragged edge of the storage container, and then stitches it up herself.
There is also a scene where she consumes her own bloody placenta.