Moving to the Dominican

Welcome to the forums. Your husband is Dominican,  he doesn't need citizenship he already has it.  Simple.

You can get residency, then later citizenship via  family reunification.  You are one of the easiest to actually do.  Go read the thread on residency as your part is covered there.  His is not.  For him,  does he still have his Dominican passport and Cedula or did he let them lapse?

You do not need an income to qualify but it always helps.

I have been a resident since 2002,  recently qualified to become a DR citizen through marriage.  Neither process is simple so please be prepared before you enter the DR for the residency process.  There are things you will need to do, like the proper visa at the DR consulate in your home country and various other documents in exactly the correct format, translations, apostille's etc.. Simple?  Not any more.

For my recent citizenship qualification through marriage, I was asked to show income, by the way.

Like planner said, he doesn't lose his citizenship. He just need to get a legalized birth certificate to proof he's Dominican.
The authorities are focusing through all the stages of the process (visa, residence and naturalization process) to prove you won't be a burden to DR so prepare to show that both of you have assets.