In the case of a spatially flat Friedmann-Lemaître-Robertson-Walker Universe in f (R)-gravity we write the Wheeler-DeWitt equation of quantum cosmology. The equation depends upon the functional form of f (R). We choose to work with four specific functions of f (R) in which the field equations for the classical models are integrable and solvable through quadratures. For these models we determine similarity solutions for the Wheeler-DeWitt equation by determining Lie-Bäcklund transformations. In addition we show how the classical limit is recovered by the similarity solutions of the Wheeler-DeWitt equation. 95.35.+d, 95.36.+x