With an average of 0.96 points per game so far, Luton are on pace to achieve 44 points by the end of the season - a number that would have seen them relegated in four of the past eight Championship campaigns.
It means Luton simply must improve under whoever their next head coach may be or face the prospect of slipping further down into League One.
"Liam Rosenior kind of fits the profile we're looking for," said Harper. "[We need] someone who is more tactically flexible, who can play with a back four, and who is good at coaching young players.
"We're in a relegation battle but we have five massive games coming up. If we can take advantage of three or four of those then the outlook will look a lot rosier very quickly."
Rosenior was sacked by Hull at the end of last season despite leading them to a seventh-placed finish in the Championship.
The 40-year-old is now the head coach of French Ligue 1 side Strasbourg and would need to be prised away.
Wycombe Wanderers boss Matt Bloomfield is currently the favourite with the bookmakers, having steered the Chairboys to second in League One so far, including a 19-game unbeaten run between August and December.
"You can understand it because he's done a great job at Wycombe," said Doyle.
"They don't have the best resources in League One and he's got them second in the table, and have been top for a number of weeks as well, playing some lovely football.
"He's a young up-and-coming manager and the type Luton like – they don't tend for go for someone who has been at different clubs."
Other coaches being linked with the role include David Wagner, Gary O'Neil, Steve Cooper, Stephen Robinson and even two-time former boss Nathan Jones.
"The first time he left Luton, he left under a cloud and the board were savage in what they said about him – and yet they brought him back for a second time," added Doyle.
"When he left the second time he left on very good terms.
"People have been saying to me 'he won't go back there again', well, they had him back last time and this time around he is still liked by the club, so it could easily happen."
Whoever comes in has big shoes to fill, regardless of Edwards' ultimate downfall at Kenilworth Road.
Harper added: "We've lost the man who gave us the greatest memories we could ever have had."