DNA barcoding and real-time PCR
You've done a pretty decent job of answering your own question, but there are a few things that can be elaborated on.

The general convention is to use the mitochondrial Cytochrome C Oxidase 1 (COI) gene for barcoding animals and chloroplast genes (rbcL, matK, and trnH-psbA) for plants. The three biggest reasons for selecting these genes are 1) their ubiquity; 2) the presence of many copies per cell, so it's easier to PCR amplify the sequences; and 3) mitochondrial and plastid DNA has a much higher mutation rate than nuclear DNA, making it possible to uniquely barcode very closely related organisms. This method is incredibly sensitive, reliable, and easy. The original DNA barcoding publication can be found at doi: 10.1098/rspb.2002.2218

Thanks to the efforts of consortia like CBOL, BOLD and iBOL, there are now many millions of reference sequences databased, covering pretty much any multicellular organism you are ever likely to encounter (assuming you don't work on a deep-seq sub or something).

As you say in your post, there are significant limitations to using qPCR to identify species. You have to know beforehand what it is you are looking for, and you are left with a simple yes-no. This is not to say there is no place at all for qPCR in the species identification game, however. The method is very fast, and in cases where you are only interested in detecting a single species or small number of species, it's much more convenient than getting the DNA sequenced (for example, during quality control in a meat processing plant, doi: 10.1080/02652030701584041).