If you can purify a plasmid containing the gene of interest in usefully large quantity, and if the affinity of the peptide for the DNA is high enough, then you can test for binding of the peptide in a high-throughput format with fluorescence polarization, which has the advantage that it can sometimes be done in a very small volume. Even 1 µl is possible with the right equipment if the signal is large enough.
The peptide is prepared with a fluorescent dye attached. The fluorescence polarization of the dye increases when the peptide binds to the much larger DNA. There are 2 important limitations: (1) getting enough of the DNA and (2) getting a big enough change in polarization.
If your gene is part of a high-copy-number plasmid, large-scale plasmid preparation may be feasible. The affinity of the peptide DNA interaction must be high enough (e.g. Kd ~ 10 nM) to allow the plasmid concentration to be low enough to make supplying it feasible. The peptide should be labeled with a bright fluorophore that gives high polarization changes, such as BODIPY-FL or BODIPY-TMR. The shorter the peptide the better for this application.
I have experience with an assay like this that used an oligonucleotide binding to a plasmid. The assay was used for a high-throughput screen of several hundred thousand compounds.