Your shirt needs( ) ,you'd better have it done today.

很显然答案错了。

B 不会吧，一定是 A:
Your shirt needs ironing, you'd better have it done today.

我也肯定是A
这里完全可以用动名词！

因为衬衫是被 熨烫 的所以要被动语态

need to be ironed = need being ironed

要用被动语态，衬衫不能自己熨自己