Is it permitted to quote something with informal language, like an interview excerpt with 'haha', in a thesis?
You should consult with your advisor about conventions in your field.  I think generally, people lightly edit interviews such as these, so if the laughter isn't revelant to what the subject is saying, you can leave it out.  If it is important, you don't have to onomatopoetically transcribe it as "haha."  You can write 
"[laughter]" or "[interviewee laughs]."