K.L.
You can definitely start disciplining her now, and you should. I don't recommend using the crib or her bedroom for time out because you don't want her to associate bedtime or naptime with being in trouble. I suggest sitting her on a "naughty step" or get a time out chair (just any chair that you use strictly for time outs).
When she does something wrong, firmly say no, and sit her in time out and say "its not nice to bite/hit/etc". Then when the time out is over tell her again "you had to sit in time out because you bit/hit/etc and that's not nice". As her language develops, teach her to say she's sorry to whoever it was that she hurt or for the action that led to the time out.
Consistency is the key in handling behavior. I would imagine the daycare has a similar policy for behavior. Make babysitters, grandma, etc who may be caring for her aware of the rules and consequences.