My advice would be to rent a car! Taxis are pretty epensive as it's a decently long ride, so your alternatives would be the shuttle services, etc., of which there are several.
I have before, on trips to DL, rented a car at LAX for 1 day, used it to drive to Anaheim, check into my hotel, do some light grocery shopping, etc., and then return it within 24 hours to the car rental location of the particular company in Anaheim. National, for example, as a location just west of Harbor on Katella (backs up to the Carsland construction site). Drop the car there and then walk to Disneyland. You can probably rent the car for around $50 for the one day. Depending on how many people you have, that may be cheaper than the shuttles.