The grammar is correct.
The meaning is slightly odd, as asking "Do I xyz?" asks whether the speaker (I) does someing in the simple present. This tends not to indicate a willful action, but most "I" questions are about actions that the speaker is doing at will.
This is odd because the questioner should know about their own actions. It is possible to use the simple present tense when asking about actions that are required.
Do I go home now?
Is is time for me to go home, whether I want to or not.
May I go home now? (or "Can I" or "Could I..")
Please give me permission to go.
Shall I go home now? (or "Should I...")
What is your opinion on whether I choose to go home now or not? Since you normally have some choice in your actions, it may be more common to ask for advice with "shall" or "should".
You say you are asking for "permission". And so you would normally ask "Can I", "May I" or "Could I".