Curtailing my Angry Baby Girl?

My five month old is one feisty little cuddle cake. She has a temper and violent streak just as bad as mama. Don't get the wrong idea...I HAVE NEVER been violent with her or around her or since she came in my tummy. She pitches a fit when feeding time is over, or whenever we are clipping her into anything (IE: bouncers, swing, car-seat) and especially when the toy she wants is out of reach. She shoves my face away when she is mad and will kick at me. If I don"t spoon-feed her fast enough she gets really upset and will kick and scream. Is she too young to be having these kind of tantrums? I know ask my pediatrician, but is this normal?-Her daddy says she has me wrapped around her finger, which is true...I adore her! But I am worried she is developing bad habits...and how could I curtail this mini anger management case?