Your baby motor skills develop much faster than her ability to speak. Most babies, for example, discover how to wave (around 9 months) and point (by age 1) long before they can say "bye bye" or "look at that!"
Giving your baby the tools to express herself may help cut down on her frustration. While baby signing doesn't promise to eliminate tears or tantrums, babies this young have been taught to "sign" successfully.
To begin, try using a hand signal every time you use common words such as "book" (open your palms with your hands together) or "hungry" (put your fingers to your lips). Later on, your baby will be able to express more complex ideas such as "I'm done with my juice" with a simple gesture such as putting her palms up at shoulder height.
And don't worry: Signing won't interfere with your baby's progress in learning to speak. In fact, it may actually help develop her language skills.
Your baby may favor one hand for a while and then switch to the other. But you can't really tell whether she's a lefty or a righty until she's about 2 or 3 years old.
Don't try to influence your baby's hand preference (it's determined before birth). Forcing her to use her right hand when she's really a lefty, for example, may confuse her and lead to problems with hand-eye coordination, dexterity, and handwriting down the road.