If you just want to quantify total miRNA amounts, not any particular sequence, I think the tried and true way is always running on a polyacrylamide gel and staining. You can use Sybr, SybrGold, or radiolabeling. Is best to use a 200 nt cut off filter to get rid of large mRNAs and you'll need a high percentage acrylamide gel. You just look for the band at 21 nt. If this sounds useful to you I'll upload some papers/protocols for you. Below is a protocol for a marker control that gives you an idea of that protocol.
You cannot use random hexamer approach, you will need to work with a specalized miRNA cDNA kit i.e. poly-A tail approach. I've used the polyA approach coupled with SYBR green chemistry to amplify miRNAs that are ~100 reads by NGS analysis but not reliably. However, for template that are mid and high in copy numbers (