I didnt take any classes during summer 1 term and used it to finish studying for the DAT. I had hoped to take it around around the beginning of May of the year I applied (this year), but ended up taking it june 10th. The idea was to take it early enough so that I could still take a retake in Aug if I absolutely needed to. So if you can manage it, try to take it before June.
I would try to time it right after taking Ochem II (assuming you've taken an equal amount of bio classes along with your chemistry). Plan your classes around the DAT, not the other way around. So if you are still a freshman/soph, try to take bio/chem classes every semester because they will help you on the DAT. Some take it earlier in their undergrad, but I felt like i really didnt have to study much after taking classes like cell bio, molecular, evolution, ecology, anatomy, physiology.