If the baby was born in the DR, to a Canadian parent, you need to go to the PP Consulate and request the Application for Citizenship Certificate from Outside Canada. (note this document is not available to download from their website)
You will have to have the original birth certificate, that states one of the parents is Canadian, officially translated, a copy of the Canadian Birth Certificate of the parent, 2 pieces of govt ID, plus $75CAD.
Yes the papers can be dropped off at the PP office.
Once you get the papers from the consolate, its quite easy to follow the instructions.