The teams were paired today in the last eight draw at Hampden and they are currently pencilled in to play on September 18 or 19 at Ibrox.
It will be the third meeting of the teams in just over four years after their 2008 Scottish Cup final clash and a League Cup tie at Palmerston Park in September 2009.
Having won four of their five competitive games so far and drawn the other at Peterhead, Gers have made a decent start to their campaign on paper.
But they have suffered from inconsistency to an extent and their performance levels haven’t always been at the level expected.
That has been put largely down to the uncertainty over the club’s status during the close season, which in turn resulted in no formal warm-up schedule.
But with four more fixtures to play before the Doonhamers come to Glasgow, Jardine feels there can be no excuse for not making it to the semis.
He said: “It’s a home draw which I think everyone will be delighted with and the supporters have been fantastic for us so I’m sure we’ll get another really big crowd.
“They will create another carnival atmosphere but we’ll have to give Queen of the South respect and it will still be a difficult game.
“We’re still bedding in and hopefully we’ll have some new players in before that game comes along.
“The biggest thing with us now being in the Third Division and having the players we’ve got is that we show the right attitude.
“I’m quite sure Ally realises that and if our players do what they are capable of, their skill will see them through.
“We would have liked to play about six friendlies in the summer but we’ve still not played six games yet.
“Some of the players aren’t at 100 per cent yet but they are getting there and I would imagine by the time we play Queen of the South, we’ll all be up and running.”
That Scottish Cup final four years ago came at the end of the famous campaign which saw Rangers play 68 competitive matches and reach a UEFA Cup final.
They were on their last legs by the time they played Queens and sneaked a 3-2 win courtesy of Kris Boyd’s double and a DaMarcus Beasley strike.
When the teams last met, it was Nacho Novo who got the winner after Steven Naismith’s opener in Dumfries.
Jardine added: “I remember the season we met in the Scottish Cup final was a really hard one for us with the amount of games we played.
“At one stage it looked as though Queen of the South were going to win the game here and Kris Boyd got us out of trouble.
“It was a really good occasion and Queens will have nothing to lose this time. They will relish coming to Ibrox and playing in front of a big crowd at a great stadium.”