Both players had knee surgery over the pre-season and were eased into match practice late in the NAB Challenge series.
Cooney, 23, didn't complete his first full training session until earlier this month.
Coach Rodney Eade said the pair would travel to Perth this week but Cooney was the only definite starter after Murphy sat out Tuesday's training session at Whitten Oval.
"Murphy will make the trip. He'll be going over, but whether he'll play only time will tell," Eade said.
"He trained reasonably well yesterday (Monday) and our main session is Thursday so he'll train again then as we didn't want him training two days in a row. It looks like Adam will play because he's pulled up pretty well."
Eade said defender Tom Williams and forward Scott Welsh would sit out the season opener after limited pre-seasons.
"I've always said Tom would miss round one. He's played the last couple of games but he's more likely to play round two," he said.
"Welsh hasn't played a lot of footy and he was ill for about a week and that set him back a bit, so he's the only one who definitely won't play."
The Dogs' coach ruled out any of the club's young guns making their senior debuts this weekend but said second-year player Callan Ward would line up.
He also said the coaches were prepared for Fremantle forward Chris Tarrant to continue his pre-season experiment of playing in defence.
"It wouldn't surprise me if he played both ends of the ground. A lot of players nowadays can play both ends."
Dream Team watch – Adam Cooney is rated a $410,000 midfielder in Toyota AFL Dream Team 2009.
