Any national from a country whose citizens enter without any visa requirements or with a tourist card (Purchase upon arrival at the airport for 10USD) may stay in the DR as long as they want to provided that they do not work. When they leave the country they must pay a relatively low fine if their staying in the DR lasted for more than 3 months ( Fine depending on the length of the staying) Citizens of all the countries of the EU are required to buy a tourist card. So you may easily stay 6 months without any visa requirement.
I do not know exactly if the volunteer work you will do is considered a job.The DR immigration law says that foreigners who want to work in the country do need a residence permit. So far the employer had to apply for the residence permit with the Direcci?n General de Migraci?n in Santo Domingo, but lately a presidential decree has been issued saying that all the applications for provisional residence permits (valid for one year preliminary to the indefinite one) must be filed with a DR consulate in the country of domicile of the applicant. I do not know if these rules already apply. You should enquire with a DR consulate in your country or ask this question to Mr. Fabio Guzman in the DR 1 legal forum.
Get your Tourist Card, do your charity work and be quiet. You will find a lot of hands stretched out looking for money of youstart asking too many questions. You will be legal for six months...if you need more you can request an extension.
Tourists entering on a tourist card may stay indefinitely
If you decide to do your charity work without a permit (in case you need one) as long as you are a tourist you can stay in the country for an indefinite period. You do not need to ask for an extension when the six months period has ended. You will only have to pay a fine when you will leave the country but paying that fine will not prevent you from entering again as a tourist on a later date.