If a 1 year old child usually wakes up in the middle of the night, is it normal or does she have a problem?

Likely norm behavior. Most 1 year olds wake because they are used to it, and getting secondary gain, like seeing you or eating. Perhaps they aren't used to soothing themselves to get themselves back to sleep. Teething can wake them up, and colds or viruses can be irritating. Discuss this in depth with your pediatrician, as there will be clues what the real story is.
Peds sleep. All children wake up briefly several times an hour. Most go back to sleep immediately. Why is your child becoming fully awake? Ways to promote sleeping through the night include: 1) minimize napping during the day 2) promote physical activity (minimize tv) 3) make the room completely dark 4) make the room quiet or have a white noise such as a fan or sound machine 5) avoid caffeine entirely.