Like many verbs followed by up, the meaning of dress is slightly different from dress up.
To dress someone is to put clothes on them. Presumably, the author can dress herself here, but in other contexts, it might refer to selecting or purchasing clothes for someone or helping them put them on.
She hadn't expected much from the Army except to get her out of the town and to dress her in green.
Her mother, obsessed with fashion, always dressed her in the latest styles.
To dress up and to dress something/someone up refer to specific activities as opposed to the everyday wearing of clothes. As OALD defines it:
dress up to wear clothes that are more formal than those you usually wear
There's no need to dress up—come as you are.
dress up | dress somebody up to put on special clothes, especially to pretend to be somebody/something different
dress something up to present something in a way that makes it seem better or different
To have a little sister to dress her up suggests either playing dress-up as children (wearing adult clothes or costumes for playing make-believe) or to make her up with fancy or formal clothes for special occasions.