9 month old Temper Tantrum?!?!

Is it really possible to have a temper tantrum this young? It really seemed like it. I was getting ready to put baby down for bed and was putting a onesie on her real quick. Well she started to get mad I'm assuming because she is tired and she doesn't ever like to cooperate with changing of clothes or diapers. So I'm reaching my hand across her chest to pull her arm out of the sleeve and she bends her head down and bites me ( she has 4 teeth). I tell her no, she does it again. I repeat this proves probably about 3 more times because I'm in shock she tried to intentionally bite me. I even said owwww! And jumped. She didn't care. After she kept biting me I lightly tapped her forehead and she proceeded to bite me. After that I picked her up and laid her down in her crib as it was time for bed anyways and she went into a full blown fit. Kicking and screaming bloody murder (no tears). Eventually she calmed down and went to sleep.

She goes into full on meltdowns when I walk out of her sight for a minute sometimes or if I have to change her diaper. I try to distract her while changing her and it doesn't help usually.

Anybody else's baby do this or do I just have a very "strong willed" baby? Lol