You can - after considering the professional and financial consequences and making sure you specify your reasons in writing - but I don't think you're at the point where that needs to happen. At least, not yet.
It's worth exploring with your manager (who may not be your immediate supervisor, but involve them too if that's the case) whether there would be any way you could continue to work there - even if just for the notice period. Some ideas might include duties that don't involve exposure to the product, or the employer switching to a different cleaning product. Document this discussion. Make a note of the brand name of the cleaning product - it's possible that others elsewhere may have experienced similar symptoms.
If there's no reasonable adjustment the employer can make, your health comes first. The employer is likely to understand this, and may suggest no notice period before you do, in which case you'll have left by mutual agreement.
If the employer appears not to understand, you'll have written evidence that you made every reasonable effort to fulfil your obligations.
Using the approach that you want to stay (even if just for the notice period) but that you can't is likely to give the best outcome.