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To make your moldings look better I would suggest that you install another smaller base molding over the original molding to mask the rough edge along the bottom of the existing trim already installed. You can get real thin and simple base trim, paint it then nail it into place. Be sure to bring it down tight to the floor so when the new carpet is installed they can bring it tight to the new trim so it looks good.
On another note. While I understand you are looking for carpet in a small child's room. I suggest that you rethink that. Carpet holds all sorts of allergens and mites. All which small children are exposed to.
Think of it like this. Kids are in another breathing zone then us adults are. They spend all of their time rolling around on the floor. Picking up all the dust, chemicals and spores that have settled out of the air.
The best thing to do is to use a wood floor with an area rug that you can remove and properly clean or dispose of when it gets dirty. They make all sorts of kid style rugs with road patterns, and things kids love. As they outgrow simply throw away.
A great book I would suggest you get to learn more about a healthy home is called "My House Is Killing Me" I always suggest that book to my clients so they can have a better understanding of the environment within their homes.