Is this your biological child?
Is your son travelling on an independent passport or is he listed on your/your husband's passport?
Are you all travelling together?

Answers to the above questions can help giving you a clearer answer.

Contact the Qatari Embassy in Washington, DC and explain your situation.
In practice you can get a visa for your son from the Embassy, once you arrive in Doha and you have your residence permit his entry visa can be transferred to a residence permit under your husband's sponsorhip, ie your husband will handle the formailities not the company.