For customised qPCR you make primers and perform something called a Sybr Green assay
The sybr green binds to dsDNA as it would for gel based assays: Specific targets and non specific targets alike
Thus, specificity can be an issue
To elaborate, sybr green assays are cheap and flexible but sufferers from the same disadvantages as making primers for gel based RT PCR, i.e. primer dimers non specific bands and having to optimise PCR conditions; or primers simply not working
In contrast you can order something called Taq Man probes: These are dye labelled probes which have been made and optimised and are therefore specific
They however expensive compared to making primers for sybr green based qPCR (which are unlabelled & designed identically to standard PCR primers)
nearly always order from outside. Unlike 10 or more years ago they are cheap and crucially outside companies offer QC spec that many internal facilities do not or indeed cannot. This is why internal facilities are starting cease Oligo synthesis
Eurofin and Sigma for example both offer quick cheap and high quality primer synthesis. I hope this answer addresses your question