The viscoelasticity of hydrogel networks formed from the low-molecular-weight hydrogelator Fmoc-tyrosine (Fmoc-Y) is probed using particle-tracking microrheology. Gelation is initiated by adding glucono-delta-lactone (GdL), which gradually lowers the pH with time, allowing the dynamic properties of gelation to be examined. Consecutive plots of probe particle mean square displacement (MSD) versus lag time tau are shown to be superimposable, demonstrating the formation of a self-similar hydrogel network through a percolation transition. The analysis of this superposition yields a gel time t(gel) = 43.4 +/- 0.05 min and a critical relaxation exponent n(c) = 0.782 +/- 0.007, which is close to the predicted value of 3/4 for semiflexible polymer networks. The generalized Stokes-Einstein relation is applied to the master curves to find the viscoelastic moduli of the critical gel over a wide frequency range, showing that the critical gel is structurally and rheologically fragile. The scaling of G'/G '' as omega(0.795 +/- 0.099) approximate to omega(3/4) at high frequencies provides further evidence for semiflexible behavior. Cryogenic scanning electron micrographs depict a loosely connected network close to the gel point with a fibrillar persistence length that is longer than the network mesh size, further indications of semiflexible behavior. The system reported here is one of a number of synthetic systems shown to exhibit semiflexible behavior and indicates the opportunity for further rheological study of other Fmoc derivatives.