The footbridge has become the focus for hundreds of tributes since a vintage Hawker Hunter jet crashed on to the A27 on 22 August, killing 11 people.
Petition organiser Charlotte Taylor said it was important for the community to note the significance of the event.
"It's really touched so many people," she said.
Councillor Neil Parkin, leader of Adur District Council, said there were also plans for a permanent memorial to the victims.
He said: "We're looking at doing a remembrance walkway from the end of the toll bridge, down the riverbank to Adur Rec, and building a permanent remembrance garden and some sort of memorial."
Mr Parkin said it would first have to be discussed with the next-of-kin.
Inquests into the deaths of the 11 who died were opened and adjourned on Wednesday.
A pre-inquest review has been scheduled for 22 March, with the full inquest expected to take place in June next year.
Police said they have no reason to believe more than 11 people died in the crash.
Pilot Andy Hill remains in a critical but stable condition at an unnamed specialist hospital.
The Air Accidents Investigation Branch (AAIB) is studying the wreckage of the 1950s' RAF jet to determine the cause of the disaster.
What we know so far about the air disaster
Profiles of the victims
'Like a bomb exploding' - eyewitness accounts
The air crash in pictures
Jet restrictions announced
Almost 3,000 people have signed a petition calling for the Shoreham Toll Bridge to be renamed The Bridge of Flowers following the airshow crash.