应该是I am going to go shopping 。go shopping 是词组:购物,根据be going to do,这个词组是充当do的成分的,如果是I am going shopping,意思就变成“我正在购物”。
I am going to go shopping对照:be going to do sth.
I am going to go shopping
是i am going shopping
I am going to go shopping.