It's true you haven't made a first date yet and you are 1 million steps from calling this a committed relationship but let her decide if the date should go on or be outright canceled.
Starting a relationship (temporary or not starts a road of trust by saying 'You could be nuts and I don't plan on emotionally supporting you if we do start a relationship beyond a one or two date period).
If you drop the date? That's fine and your prerogative to do so. Be honest about it. Also, don't expect to date her when this crisis partially or fully resolves or just gets worse. That's not going to help anyone in this equation.
If you do go on the date? Don't hang it over her head like the Sword of Damocles. Just go to the date. Do the date activities and be there to support her if any lingering issues remain.