Public Health Agency of Canada says: “Antimalarial medication may be recommended depending on your itinerary and the time of year you are travelling.”
If you can you should check with your GP or Travel Clinic before the journey. Currently the recommended preventative is chloroquine. Use mosquito repellent containing DEET, especially at dawn and dusk and whenever possible wear clothes covering all your body.
Tap water is not potable. In some places locals will tell you it is. And it might be fine for them but chances are not for you and you probably don’t want to find out and spend the rest of your holiday looking for the closest bathroom.
Bottled water is widely available throughout the country and it is recommended that vacationers drink at least 10 glasses or about 2 liters a day to avoid dehydration.
Hurricanes occur regularly in in the Caribeean between June 1 to November 30. August and September usually have the most hurricanes. Hurricanes are the greatest natural threat to the Dominican Republic. In 1979 two hurricanes left 200 thousand people homeless. Nonetheless a significant damage is done by hurricanes almost every year and typically thousands of people need to be evacuated. Hotels are usually well prepared for this emergency.
Here is the animation of the biggest hurricanes in the last 100 years. As you will note, quite a few went straight through Punta Cana.
Moderate earthquakes struck the Dominican Republic pretty regularly but typically no damage is reported. In theory earthquake in Punta Cana can happen, but the place has not experience a serious shaking of ground as long as people that live there can remember. Also Punta Cana resort buildings are built better than most buildings in the Dominican Republic and thus even during a serious earthquake they have higher chance of not being impacted.
The Dominican Republic is a big country and so for example 2010 deadly earthquake in Haiti was not felt in Punta Cana.
There were two serious earthquakes in the last century in the Dominican Republic. In 1946 the earthquake of magnitude 8.0 originated in Samaná province and left 20 thousand people homeless. The last significant earthquake (6.4) was registered in 1984.