The Google Books results come out quite strongly in favor of omitting the comma, but it depends on how long the “Oh . . .” phrase is. Two-word versions usually do not have it, while longer ones like “Oh for the love of . . .” more often do.
You should inspect these for yourself. I went the first twenty pages of “Oh dear”, and certainly found some with the comma. Not many, but some.
As you can see, there are exceptions, but most do not use use the comma after the oh. One old but interesting examples is the line from Shakespeare’s All’s Well That Ends Well, because you can find it variously punctuated.
- O, for the love of laughter, let him fetch his drum;
- Oh, for the love of laughter, let him fetch his drum ;
- Oh ! for the love of laughter, let him fetch his drum ;
The old hymn doesn’t usually use a comma, either:
- O for a thousand tongues to sing my dear Redeemer's praise
I suggest omitting the comma, but I don’t know that there is an actual rule here to cite.