Recently, fractional-quantized Hall effect was observed in suspended graphene (SG), a free-standing monolayer of carbon, where it was found to persist up to T=10 K. The best results in those experiments were obtained on micron-size flakes, on which only two-terminal transport measurements could be performed. Here we address the problem of extracting transport coefficients of a fractional quantum Hall state from the two-terminal conductance. We develop a general method, based on the conformal invariance of two-dimensional magnetotransport, and employ it to analyze the measurements on SG. From the temperature dependence of longitudinal conductivity, extracted from the measured two-terminal conductance, we estimate the energy gap of quasiparticle excitations in the fractional-quantized ν=1/3 state. The gap is found to be significantly larger than in GaAs-based structures, signaling much stronger electron interactions in suspended graphene. Our approach provides a tool for the studies of quantum transport in suspended graphene and other nanoscale systems.