Fifteen questions can give a quick, useful rough indication, especially if the quiz clearly says it is not an official assessment. But the result will be sensitive to a few questions, and grammar, reading, and vocabulary alone don’t show the full B1 profile—listening and speaking are missing.
To improve it, use several questions per skill, include a range of difficulty around the B1 boundary, and make the reading tasks test understanding of connected text rather than isolated details. Pilot the quiz with learners whose levels are known, then check whether the questions and score bands distinguish levels consistently. You could also report a range or skill-by-skill breakdown instead of a definitive “B1” label, and explain what each result means.