Another suggestion for taking that baby out of the car seat. That baby looks pretty big too, so she may be able to sit up which opens the door for some poses. If she can't sit up, at the very least she can lay on her tummy and hold her head up.
My first thought when I saw the first one was that it was too soft. I'm not sure if the fuji finepix camera you were using offers control over the settings, but this was shot at f3.1. If you can bump that up to f8-ish it would help with the depth of field.
As far as composition with what you have, I'm a stickler for some of the basic rules, like the rule of thirds. In the first picture I'd move the head a little more to the left leaving at least 2/3 of the frame to the right of her head. When subjects are centered in the frame it becomes a little too static for me.
Having said that, I kinda like the idea of centering the head in the second shot because of the symmetry. If I HAD to shoot that picture, I would try to get the baby to look straight up rather than angling the head. If you could accomplish that then you'd have quite a symmetrical shot.