Ally McCoist's side has won their last two away matches in the league, against Clyde at Broadwood earlier this month and against East Stirlingshire at Ochilview last Saturday.
Those performances and results suggested the Glasgow giants have, at long last, addressed the problems they were experiencing on their travels in the bottom tier.
The Gers dropped points to Peterhead, Berwick Rangers and Annan Athletic and, worst of all, lost against struggling Stirling Albion on the road at the start of the campaign.
With so many young players being thrust into the fray –Lewis Macleod, Barrie McKay and Ross Perry have all been regular starters – McDowall was not surprised that they have faltered at times.
He is hopeful that this new-look Rangers team – now two points clear of Elgin City with a game in hand – have now learned how to win away at this level.
But McDowall reckons a win over nearest challengers Elgin in the live ESPN match at Borough Briggs on Sunday – an outcome that will send then five points clear – will show they have come of age.
He said: "Every game is a good barometer of where the team is at the moment. They are all good teams in this division. You don't get an easy game off of any of them.
"But the fact that Elgin are sitting on our coat-tails certainly makes it more interesting.
"To be fair to Ross Jack, he has done a good job up there. They are a good side, Elgin.
"They pass the ball about well. They are also committed. It will be a tough game. But we know that is what we are going to get every time we take to the field.
"We need to keep raising the bar and if that means beating Elgin away and creating a gap between ourselves and them at the top of the league table then that is what we need to do."
McDowall is hopeful youngsters like Fraser Aird, Darren Cole, Robbie Crawford, Chris Hegarty, Lewis Macleod, Barrie McKay and Kal Naismith have matured as a result of their first-team experience this season.
At times this term, the Rangers kids have looked unable to cope with the uncompromising physical nature of the game in the Third Division – as well as with their surroundings at some of Scottish football's less glamorous outposts.
Yet, against Clyde and East Stirling they were often subjected to a fair few meaty challenges from bigger and stronger part-time opponents and they stuck to their task manfully.
Creating a small cushion between themselves and Elgin this weekend – the first time this season they have been in that position – would be a major milestone on the long road back to the top of the game in this country.
McDowall reflected: "It was only a matter of time before we got the win away from home in the league. To be honest, we weren't that concerned. We knew it would come.
"But it was just the players learning how to deal with it. It was a big deal. There was also a lot being made of it because it was Rangers.
"That goes with playing here. You have to accept that and learn how to deal with it. The way to deal with it is to go and win the games so you don't get a bad reaction in the media.
"But I think they are starting to find their feet. They are getting better. They are starting to be more aware of what they are up against in away games."
Even the experienced players at the club – the likes of Neil Alexander, Ian Black, Lee McCulloch, Dean Shiels and Lee Wallace – have found dropping down to the Third Division a shock to the system this season.
Black, who joined from Hearts in the summer, has been outspoken about the treatment he has been subjected to by rival players at times and at the lack of protection he is being given by referees.
McDowall, though, has urged the player to concentrate on his own game and in helping Rangers extend their lead in the Third Division.
He explained: "The bigger deal he makes of it the more they will target him. That is what these boys do at this level.
"The East Stirling player Paul Quinn disagreed with what Blacky said and I tend to agree with him.
"He said the boys are late in the tackles at this level because we move the ball so quickly. They (opposition players) are getting there as early as they can – it is just not early enough unfortunately!
"The thing to do is move the ball even quicker. That is what Blacky has got to do. Obviously he is looking for referees to give himself a wee bit more protection. Personally, I think he should just get on with playing football and stop worrying about it.
"We need to concentrate on the job in hand – getting out of this division. We need to focus on winning the Third Division."