"I want a big calendar."
Yes it should be since 大きな is a な adjective immediately followed by a noun.
In this sentence 欲しい (hoshii) want is an adjective (even though it's a verb in English).
Japanese structure with an adjective is usually:
subject は thing the adjective is describing が adjective です。
So in this case, "I" is the subject, the adjective is "want", and the thing that I want is the "calendar".
Watashi wa karenda- ga hoshii desu.
So even if we leave out 私は (watashi wa) and add 大きい (ookii) as an adjective to describe the calendar, the thing that is being described by the adjective 欲しい (hoshii) needs が.