There may be some behavioural insights (or behavioural economics) research into this, but I would suspect the questionnaire first is a better way to go.
My thinking is that
- you can start initially by collecting their name and email address
- people may hesitate to upload a photo if it's the first thing they're being asked to do
- people are more likely to add a photo because they're already somewhat committed once they've completed the questionnaire.
However, if it was me, I would also have it designed in a way that they have a number of steps to complete and they can select the order they do them in (except that the first step must be capturing their name/email). This way they can choose to upload a photo first if they happen to have one handy they like and do the questionnaire later when they have more time.
You just need to make sure it's clear that their registration isn't complete until they've done both. They can come back later if needed to complete the process, and since you already have their name/email, you can send them a reminder if they haven't completed registration after 24hrs.