If the subject is fast (and one year olds are) and close and moving toward and away from you, very few cameras will work well with auofocus, because it takes time for the camera to focus, and your one year old moves faster than the camera.
Turn off autofocus. Get far enough way from him/her that the lens can hold sharp focus from the nearest the child will get to the farthest. (Use a depth of field chart for this. Search for them, then print one that you like - they'll all have the same numbers, but maybe you like the way one is laid out better than another one.) The more light, the smaller the lens opening will usually be, so the larger the distance the lens will maintain focus.) Then focus on something about halfway between the two.
Phone cameras don't work any differently than plain old cameras, digital or film. Lenses are still lenses and light is still light. Lenses still focus light the same way they did back when Matthew Brady was taking pictures of the Civil War.