Doyle's quadratic-polynomial preperiodic-point bound over quadratic fields

Let $K/\mathbb{Q}$ be a quadratic field, let $f\in K[z]$ be a quadratic polynomial, and let $\operatorname{PrePer}(f,K)$ denote its set of $K$-rational preperiodic points. Doyle's conjecture.

$$\#\operatorname{PrePer}(f,K)\leq15.$$

Computational investigations found the same bound in extensive searches, but the conjecture remains unproved in general.