go out for a date --> I'll go out for a date. I'll be back soon. go on a date --> Derick and I will go on a date.

'go out on a date' ' go on a date' Both are correct and the only difference is the additional info 'to go out' which is redundant and could be left out in the context. Here the date is already determined.The person is going out with a specific date. " He is going on a date with Jane tonight." 'go for a date' is also correct and means attempt to date someone or intend to do so with a tendency to make it happen. Here 'go for' is a phrasal verb. There is no specific date , but the person attempts to look for one and make it happen. "You are single for a while now ,why don't you go for a date?"

I'm going on a date. I'm going out on a date. I'm going out for a date. All three are fine.