When my daughter sleeps, her breathing is fast and she has a high fever. Should I take her to the hospital?

Measure temperature. Determine what the temperature is. If her body feels warm but not the forehead you feel with the back of your hand and measured then it is not fever. Infants breathe faster than adults. If truly a fever and labored breathing then it is best to have her evaluated.
Yes. A fever suggests an infection. If she is breathing fast it is likely a respiratory infection that has triggered either expiratory wheeze such as asthma or inspiratory stridor such croup. I would definitely take her to er if she has breathing problems.