mature miRNAs are around 22bases (range: 16 to 32): I think there is no need to assemble. Reads potentially represents complete mature miRNA's, if small RNA extraction protocols are followed before sequencing.
If you don't have reference genome. Best way to get potential microRNAs is to map the reads to the complete miRbase ; say using miRNAKEY; And also map using mirdeep2 or other tools to the nearest homologous genome whose sequence is available. Then blast or blat the potentials reads obtained to the NT or EST databases to see if any potentials hits in the genome of your interest.