"to pick up" is said in many different ways depending on the situation (who is pickup up what and how).
The base words are 가지다, 찾다, and 데리다, but they usually combine with 가다 or 오다 in real usage, so there can be a dozen different expressions.
For your example, I'll assume 밥솥(rice cooker), as "cooker" can mean a lot of things.
A: "When do you want to pick up the rice cooker?"
1. 밥솥 언제 찾아가실 거예요? (if it belongs to the person and is waiting to be picked up)
2. 밥솥 언제 가져가실 거예요? (more general cases 가져가다 = 가지다 + -아/어 가다 = pick up; take)
B: "Can I pick it up tomorrow?"
1. 내일 찾으러 가도 돼요? / 내일 찾아도 돼요?
2. 내일 가지러 가도 돼요? (가지러 = 가지다 + -러 = (in order) to pick it up)
The root verbs:
- 찾다 = to pick up something that is waiting for you (at a business, office, etc)
- 가지다 = "to have". When combined with -아/어 오다/가다, it can mean "to pick up (something)".
- 데리다 = used for people.
Picking up something is usually said with -아/어 가다/오다 because we usually pick it up and take is somewhere.
So the full action is described as 찾아오다/찾아가다 or 가져오다/가져가다 depending on your perspective (가져오다/가다 can additionally mean simple moving/carrying).
If you're coming or going in order to pick up something, as in your example, it becomes 찾으러/가지러 오다/가다.
Here is the set of commonly used forms.
(picking up things)
- 찾아오다 = (you or someone) pick up something and bring it home.
- 찾아가다 = (someone or you) picks up something and takes it away. (i.e. they pick it up from you)
- 찾으러 가다 = go somewhere to pick up something.
- 찾으러 오다 = comes here to pick up something.
- 가져오다 = pick up something and bring it home.
- 가져가다 = picks up something and takes it away.
- 가지러 가다 = go somewhere to pick up something.
- 가지러 오다. comes here to pick up something.
(picking up a person)
- 데려오다 / 데리고 오다 = (you or someone) pick up a person and bring them home.
- 데려가다 / 데리고 가다 = (someone or you) picks up a person and brings them away.
- 데리러 오다 = comes here to pick up a person.
- 데리러 가다 = go somewhere to pick up a person.