Austin put his side ahead in the 17th minute with a volleyed strike, and he netted his second after the break by tapping in from close range to secure his side's second win of the campaign.
Redknapp told the club's official website: "Charlie was always going to score goals at this level. He's a proven scorer and took his goals well tonight.
"The first was a great finish and the second was pure striker's instinct, after a great ball into the box from Vargas. All in all it was a really pleasing night for us."
QPR moved off the bottom of the Premier League with the victory, but are still in the relegation zone after nine matches this season.