One of my questions was suggested to be a duplicate of another. I read the linked question and agree that it is a duplicate.
Should I delete my question immediately or wait? If I should wait, what am I waiting for?
No you shouldn't delete the question unless it is word-for-word, exactly the same. They are actually useful. The way you phrased your question might be the same way another person searching might phrase theirs.
If you have good answers on your question, it might be a good idea to request a merge so the answers end up on the "canonical question."
If you think it is really a duplicate, you can vote to close your question. A duplicate question is not necessary deleted, once it is closed; it is deleted when both the questions use the same phrase, but when they are not, the duplicate is helpful for who is looking for a question.
If the question were off-topic, without answers, it would be different. Still, keeping to delete your questions can give you problems. Then, except in the more evident cases (e.g. your question on Stack Overflow is "What time is it?"), I would leave the decision to the community, which will close the question if it is really off-topic, and then delete it.