We present studies of high-order harmonic generation (HHG) in laser ablation plumes of the ribonucleic acid nucleobase uracil and its deoxyribonucleic acid counterpart thymine. Harmonics were generated using 780 nm, 30 fs and 1300 nm, 40 fs radiation upon ablation with 1064 nm, 10 ns or 780 nm, 160 ps pulses. Strong HHG signals were observed from uracil plumes with harmonics emitted with photon energies >55 eV. Results obtained in uracil plumes were compared with those from thymine, which did not yield signs of harmonic generation. The ablation plumes of the two compounds were examined by collection of the ablation debris on a silicon substrate placed in close proximity to the target and by time-of-flight mass spectrometry. From this evidence we conclude that the differences in HHG signal are due to the different fragmentation dynamics of the molecules in the plasma plume. These studies constitute the first attempt to analyse differences in structural properties of complex molecules through plasma ablation-induced HHG spectroscopy.