Most insurers here do not cover for individual GP visits but if yourself or your hubby's company has group insurance, then they MAY be able to include your son. Do note that some companies may choose to cover only the employee only , employee/spouse only or not at all.
As for hospitalisation expenses, if your son is a Singaporean,you can buy a Healthshield plan from any of the main insurers here. There is a optional rider that you pay additional premium for,this rider will cover the initial deductible amount (Up to $3000 depending on the ward chosen) and also the co-insurance portion which is fixed at 10%.The basic play is payable by Medisave and the rider is payable by cash.
If you are not a singapore/singapore PR, you can also buy this plan from AIA as we are the only company that extends this plan to non citizens/PR.
You can PM if you are keen to know more?