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In this paper we propose a novel method for designing irregular quasi-cyclic low-density parity-check (LDPC) codes from Balanced Incomplete Block Designs (BIBDpsilas). The design method hinges around finding the optimum degree profile by minimizing the threshold using density evolution. The approach for designing short block length codes is robust for practical implementation and has been found to exhibit considerable performance gain that may be attributed to a good degree profile for the codes. The design takes into consideration the code rate and code length as variable parameters. The simulation results for the designed codes are compared with regular and irregular quasi-cyclic BIBD based LDPC codes and found a relatively higher performance in terms of BER.