Most likely, the problem involves sending TOO MANY COLONISTS with your colony ships. The default setting (why is this default???) is to send HALF of whatever is on the planet. That's way too much in almost every case.
Morale is a function of population relative to population capacity. More people than the planet and its improvements can handle, bad morale.
PQ15 planet can only handle about 200 million people or thereabouts before morale starts to drop. If you send half the population off a world with 3 billion and land 1.5 billion on a PQ15, morale will be awful.
One of the keys of making use of PQ13 and PQ14 planets is to send only a couple dozen millions of colonists and to emphasize building morale improvements there so they can keep up in population growth (and thus economy) with the rest of your worlds.
If settling a new colony with no improvements, as opposed to invading, if you are getting morale problems from the get-go, I'd say it has to be related to sending too many colonists. Try adjusting the number downward, never use auto-launch with colony ships, and even (when possible) adjusting for the size of the world you intend to settle. You'd want to send a lot of people to a PQ25, for instance. Even sending MOST of your people from Earth in the early game if a better world than Earth is available nearby.
I hope this helps.
- Sirian