Turkey is available at cooking level 6.
http://thesimsresource.com/article/strategy/foodguideAs the others said, make sure you are choosing Serve meal, not Have meal.
I have both dizzy2's smart serve and TJ's serve everyone hacks in my game, and I have all food choices available.
Also, the type of stove or fridge you have does not affect your cooking options, excluding the Uni mini fridge and cooktop.
P.S. When I saw the topic of this thread, I thought it was talking about bowling! I want my sims to get a turkey but they never play long enough!
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