A B737 FLC NOTES A DROP IN THEIR FUEL PRESSURE AND FUEL FLOW ON #1 ENG IN CLB MANDATING A CHANGE TO A LOWER ALT WHERE THE FUEL FLOWS READ NORMALLY ON FLT TO IAD; VA.

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DEPARTING AUS TO IAD; CLBING THROUGH FL340; RECEIVED MASTER CAUTION AND FUEL LIGHT. NOTICED 2 LOW FUEL FLOW LIGHTS ON #1 ENG. FO PULLED IRREGULAR CHKLIST; WHICH WE STARTED ON. AS I WAS STILL CLBING TO OUR CLRNC ALT OF FL350; I REQUESTED FL330 TO START DOWN. ABOUT THE SAME TIME I NOTICED #1 FUEL FLOW START TO DROP BACK TOWARDS IDLE. WE DSNDED TO FL330 WITH ALL LIGHTS OFF AND INDICATIONS NORMAL. REACHING FL330 AND A COUPLE MINS LATER; FUEL FLOW LIGHTS CAME BACK ON. ALL OTHER PARAMETERS NORMAL. REQUESTED FL290. REACHING FL290; ALL INDICATIONS NORMAL. CALLED DISPATCH/MAINT COORD AND ADVISED THEM OF SIT. FO AND I DISCUSSED CONTINUING ON AND WE BOTH FELT OK WITH GOOD WX ALL THE WAY TO IAD. DISPATCH MAINT CONCURRED AND MAINT SAID JUST KEEP AN EYE ON THE FUEL FILTER AND FUEL FLOW INDICATOR. ADVISED ATC OF OUR NEW CRUISE ALT REQUEST. CALLED DISPATCH TO ADVISE OF ALT CHANGE AND FOR NEW FLT PLAN AND FUEL BURN. I ELECTED IN AUS TO ADD 1500 LBS FUEL BECAUSE OF NOT GOING INTO IAD FOR A LONG TIME. SO WE HAD PLENTY OF FUEL; GOOD WX; AND MANY GOOD ALTERNATE ARPTS ENRTE WITH GOOD WX. FLT WAS NORMAL TO IAD; AND UNEVENTFUL (ALSO HAD ADVISED FLT ATTENDANTS ON SIT -- JUST FOR 'HEADS UP').