I personally would not be comfortable with cutting it that close. The rental car lots are all off site at LAX - outside the baggage claims area you need to board the shuttle for your particular rental company in the area indicated by the purple "Rental Car Shuttle" signs. Between landing, getting luggage, getting the shuttle and then picking up your car you can look at a good solid hour before you are on the road and headed for Anaheim. Then the drive even in light traffic will take you at least 45 minutes. That is if everything is on time. So that could see you in Anaheim by 12:30. We have landed at just after 12PM before and been in Anaheim at our hotel well before 2 but we never count on it.
My recommendation for car rental is to subscribe to whatever frequent customer plan the rental agency offers - all of them have some form you can join which is normally free of charge. That can facilitate pick up of your vehicle and save you a lot of time. We use the FastBreak service with Budget and they drop you off, you check the screen to see where your vehicle is located, you get in and drive to the exit where they verify credit card and drivers license information and off you go! Otherwise you can be waiting in a long line to see an agent.