normal heart rate for four year old is 73-137 bpm
Hello the normal heart rate for a 4 year old child is generally between 80 and 110 beats per minute just like that of an adult. If the child is in dream state or Rem sleep or is possible getting ill it can be slightly higher which may be what was going on when you checked your kiddo. If your child's blood pressure has a tendency to run low, his pulse rate will be higher to compensate for that, as well. I don't think the 134 is anything to be alarmed about, I'd check it again in a couple hours just to see what it's running at that time. If you want to get it check out for piece of mind I recommend you do just that. I Hope This Helps!
It should be between 60 and 90, though could rise up during REM(rapid eye movement) phase of sleep. Children tend to have more REM phase than adults. But it could also be sleep apnea, so you better get your daughter checked by a pediatrician. Thank You and hope it helped.