A B744 CREW WITH A PAX IN LABOR TOOK THE COMPANY DOCTOR'S ADVICE AND CONTINUED TO DEST.

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I WAS THE RELIEF PLT IN THE L SEAT IN CRUISE WHEN THE PURSER INFORMED US OF A PAX WHO WAS IN LABOR WITH CONTRACTIONS 1-2 MINS APART. WE GAVE DISPATCH A HEADS UP AND WOKE THE CAPT 1 HR EARLY. THE PURSER INDICATED IT WAS SERIOUS AND NO MEDICAL PERSONNEL WERE ANSWERING HER PA FOR ASSISTANCE. AS THE CAPT WAS GETTING DRESSED WE TOLD DISPATCH TO HAVE A DOCTOR STANDING BY AND WE WOULD CALL HIM BACK FROM AN AIR PHONE NEAR THE LABORING WOMAN. THE CAPT GOT IN THE SEAT AND I WENT TO THE CALL DISPATCH NEAR THE WOMAN. AFTER DETERMINING FROM THE DOCTOR THAT WE COULD PROBABLY CONTINUE TO ORD I WENT BACK TO THE COCKPIT TO APPRISE THE CAPT OF THE STATUS OF THE SIT. THEY TOLD ME THEY WERE UNABLE TO JOIN THE CONFERENCE CALL AND THAT THE DISPATCHERS WERE DEALING WITH ANOTHER MEDICAL EMER. BOTH THE DISPATCHER AND WE HAD BECOME FOCUSED ON THE DETERMINING WHETHER TO STOP SHORT OF ORD FOR MEDICAL ATTN AND DID NOT COMPLETE THE REDISPATCH UNTIL AFTER WE DETERMINED WE WERE CONTINUING TO ORD AND SLIGHTLY AFTER THE REDISPATCH FIX. WE KNEW THE WX IN ORD WAS VFR AND WE WOULD HAVE APPROX 30000 LBS OF GAS ON LNDG AT ORD. SUPPLEMENTAL INFO FROM ACN 520982: FUEL WAS NOT A FACTOR AS WE WERE ONLY SLIGHTLY BELOW PLANNED. WE CONTINUED TO ORD AND PARAMEDICS MET THE FLT WITH NO FURTHER INCIDENT.