Dear,
If a baby is born in Qatar, HMC will guide u in getting birth certificate for the new born...by submitting this birth certificate along with relevant details in Indian Embassy as your from India, they will give u a passport of India...In Qatar the baby holds Indian passport rather than Qatar passport though the baby is born in Qatar...Once u get passport for the baby, apply for Residence Permit in Qatar...

If everthing is done perfectly, baby can safely travel with parents to India...

The entire process takes approximately 1-2 weeks, if proper planning is done once the baby is born...