Legal Question in Real Estate Law in California

No. Even if there was gift tax owed, it is owed by the person who makes the gift, not the recipient. Giving and receiving real property can have ALL kinds of negative tax and other consequences. It is a REALLY bad idea to do that without the help of a lawyer, both for the giver and the receiver. For example it can get both of them sued if the giver has debts they can't repay. It also triggers transfer taxes and property tax reassessment. It's just a BAD idea to do without help and advice.

Also, it's not really clear from your question whether you are the current owner or the possible future owner of the house. ".....my brother quitclaim...." and "....replace my name on the title...." are conflicting clues as to which of you is the current owner.