Racing authorities are awaiting autopsy results to confirm the cause of death.
Hagley was knocked unconscious in the fall but regained consciousness before her trip to hospital for observation.
Fellow runner Pharoah Murphy was unable to avoid Shine The Armour and also fell, but escaped injury.
The race also had a third faller, Celtic Emprie, who also escaped injury.
The future of jumps racing is under a growing cloud, with Racing Victoria granting the sport a three-year reprieve last year, but making it clear that the death rate must be kept down.
However, welfare advocates opposed to the sport say the deaths so far this season were predictable.
They have called for an immediate suspension of the season.
The season was temporarily halted in 2009 after three horses died during the Warrnambool carnival.
It was reinstated after an outcry from supporters.
Last year's carnival claimed one horse.
So far, five horses have died in jumps racing and trials in Victoria and South Australia in 2011 - already topping the death toll for last season.
Animals Australia slammed the jumps racing industry following the death of the six-year-old gelding.
Executive director Glenys Oogjes described the death as an appalling outcome from the very first jumps race at Warrnambool.
"It must surely demonstrate again to the Victorian Government that jumps racing is highly dangerous, and cannot be made safe for horses or jockeys."
Oogjes said it was unacceptable that Racing Victoria would accept a death rate in jumps racing that was sixteen times the rate of flat horse races.
She called on the state premier to immediately stop jumps racing.
"The jumps races planned for the remaining two days of racing at Warrnambool must not be permitted to proceed."
Racing Victoria has set fall rates (3% of starters) and death rates (0.65% of starters) as benchmarks for the continuance of jumps racing. Even prior to the death of Shine The Amour, the 2011 season statistics were triple those imposed limits.