(1) Background: TDMQ20 is a specific regulator of copper homeostasis in the brain, able to inhibit cognitive impairment in the early stages of Alzheimer’s disease (AD) in mouse models of AD. To promote the further development of this drug-candidate, preliminary data on the pharmacokinetics of TDMQ20 in a mammal model have been collected. Since TDMQ20 should be administered orally, its absorption by the gastrointestinal tract was evaluated by comparison of blood concentrations after administration by oral and IV routes, and its ability to reach its target (the brain) was confirmed by comparison between blood and brain concentrations after oral administration. (2) Methods: plasmatic and brain concentrations of the drug after oral or intravenous treatment of rats at pharmacologically relevant doses were determined as a function of time. (3) Results: oral absorption of TDMQ20 was rapid and bioavailability was high (66% and 86% for males and females, respectively). The drug accumulated in the brain for several hours (brain–plasma ratio 3 h after oral administration = 2.6), and was then efficiently cleared. (4) Conclusions: these data confirm that TDMQ20 efficiently crosses the brain–blood barrier and is a relevant drug-candidate to treat AD.