I can say it sounds not "unnatural", but just very uncommon. It looks like you will cook THE dinner (though in this case that's not obvious, merely a slight nuance), so it would be weird if you say about dinner (which is not ready yet) like about "the dinner".
In fact, there are a lot of cases when you can use "иду/еду/лечу/бегу etc" + a verb in the perfective form. Just remember that almost all of these constructions sound uncommon or special (when you mean "THE" action/thing you're going to do).
- Куда ты едешь?
- Я еду/иду сдать документы (the documents)
- Куда ты идешь?
- Я иду отправить письмо (the letter)
- Ку да ты так торопишься?
- Я бегу сдать кровь для пострадавших (for the victims, you're a going to do a specific action for them)
If we exchange the perfective for the imperfective, it doesn't mean that "the" disappeared (it depends on context). It just means we concentrate on the process more than on the objects.