일 가고 싶어요 and 저(는) 일 가고 싶어요 are both okay. It depends on what exactly the speaker wants to say.
에 can't be used after 일. 일 가다 is similar to 낚시(하러) 가다 or 쇼핑(하러) 가다. The noun indicates the purpose or activity rather than a place, so adding 에 will make it very strange.
The phrase sounds a little odd because 일 가다 usually means going to work as part of a routine, so it would be rare for people to say 가고 싶다 for 일. Phrases like 일 가야 돼요 (I must go to work) would be more common.
Also, 일 가다 is a tradition term for older types of work. We use 출근하다 for most modern types of jobs like office work or corporate jobs.