A What your child is doing is normal, but it's also annoying. Toddlers bite and grab at things both to communicate what they do and don't want and to experiment with the reactions they get from others - and hair-pulling obviously gets an immediate reaction! This doesn't mean your daughter is abnormally aggressive; she's simply testing which behaviors are acceptable and which are not. It's up to you to teach her the difference.
Here's how: As with any annoying habit, you need to distract and substitute. As soon as you see those little hands reach for someone's hair, get her attention her by calling her name, then immediately involve her hands in a more acceptable behavior - playing a game such as peek-a-boo, or holding a toy. You can also teach her some alternatives to hair-pulling that get a more positive reaction: Take her hand and show her how to pat someone's head, stroke their cheek, or give them a hug. Tell her, "No, we don't pull hair, but we do hug and pat." And if you can identify situations that trigger the annoying behavior - fatigue, hunger, and frustration are the most common ones - you'll have a better chance of heading off problems before they arise.
A 13-month-old is too young to fully understand that pulling someone's hair hurts them - which is why it doesn't work to pull her hair and expect her to understand how it feels to others - but she can learn that nice behaviors get nice responses and annoying behaviors don't. Similarly, although your daughter is still a little too young for a "time-out," she can make the connection between grabbing something she's not supposed to and your taking it away from her. Over the next few months focus your discipline on what she may grab and what she may not. Guide her hands toward "yes touches" and away from "no touches." As your toddler grows and adds more words to her vocabulary to express her frustration, these aggressive behaviors will naturally become less frequent.