Burnett navigated the side to League Two safety after taking over from John Still in February, despite a final-day defeat to York.
Burnett's men won just one of their final nine league games but Doe is confident the current boss is the man for the job as he looks ahead to an improved season next year.
He told London 24: "I hope Wayne gets the job. He can bring in his own players and do his own thing.
"We've battled and beaten some of the bigger teams in this league, so we know we can do it.
"Obviously we want to finish as high as possible."