You can do qPCR on DNA directly if you are interested in copy number variation of a particular gene/region. If you are interested in gene expression levels then you must extract RNA and produce cDNA.
Hi, if you use column-based approach for DNA extraction as a result you always have a lot of RNA and DNA in eluate. I agree with other - the aims and targets is essential. But you can extract NA with special RNA/DNA kit, after that devide sample in two parts - 1 without RT and 2 with RT (cDNA as a result). But the majority of kits can provide you NA mix.
At first, look at your primers and be sure they can bind on gDNA as qPCR primers generally covers exons junction area. If it's not the case, also be sure that the intron will not be amplified and increase the size of the final product. If those two conditions are respected, I think you could go with direct extracted DNA (gDNA).