The highly-rated ex-Auckland Blues front-row, 30, was in the mix for Australia selection last year after impressing in Super Rugby.
Mayhew – younger brother of Carnegie captain Richard – arrived in Leeds in mid-December, but has been recovering from a torn biceps.
However, he will come off the bench and debut against Cornish Pirates at Emerald Headingley.
Stirling admitted: “He is a Premiership quality player, there’s no doubt about that.
“He was on the verge of international selection last year. His scrummaging over here will be a real development for him and a real challenge as it is for most Kiwi and Australian props when they come to this neck of the woods. But as a general ball player and around the field he’s at another level.”
Carnegie, who lifted off bottom when winning at Doncaster Knights last time out, also welcome back Wasps full-back Jacob Umaga on dual registration for the Championship contest.
Carnegie are seeking a sixth successive win in all competitions while, conversely, Doncaster attempt to avoid a sixth consecutive defeat when they head to promoted Coventry today.
They came close to beating Carnegie and director of rugby Clive Griffiths insisted: “We are not far off getting our game management correct and with that the results will come.
“We’ve seen it in all the games how close they have been. It is just we get that mad moment in matches and that causes us a bit of grief.”
The Welshman makes a number of changes as Doncaster strive to avoid being dragged into the relegation mire.
Wingers Paul Jarvis and Curtis Wilson have both suffered injuries along with fly-half Kurt Morath and lock Matt Challinor. Full-back Steve McColl comes in as do wingers Tyson Lewis and Dougie Flockhart, while on-loan Ealing Trailfinders No 10 Sam Olver makes his first start and USA lock Nick Civetta also returns.