That provides Walter Smith's men with the opportunity to move into pole position and gain the psychological advantage before Tony Mowbray's men even have the chance to kick a ball this weekend.
"We need to continue to put pressure on them," said Whittaker.
"Any time we get the opportunity to play before them, it's important we take the points and push on in the league.
"With the game being at Ibrox, hopefully that's a plus for us and the fans will get behind us and we can take the three points.
"It's important that we focus on the job in hand and that we have good results and performances over the Christmas period."
The last meeting between Rangers and Kilmarnock was marred by the performance of referee Steve Conroy.
Rangers boss Walter Smith was sent to the stand, while Pedro Mendes and Manuel Pascali were both dismissed and seven other players booked in a game both camps claimed was far from a dirty affair.
"The games between Kilmarnock and ourselves have always been well-contested and there have never been any problems," said Smith.
The Rangers boss says he is more interested in producing a better level of performance than the display at Rugby Park, where they were fortunate to escape with a goalless draw.
He added: "We have just been starting to show a level of form and consistency in performances that we hadn't shown in the earlier part of the season.
"Our previous game at Kilmarnock was a poor one from our own point of view and we were very fortunate to come away with a draw that day.
"But we have been doing better recently and have picked up our performances. I hope that's something the international break hasn't interfered with and that we can carry on the way we have been doing.
"The three international breaks we have had this year I don't think have helped any of the teams in terms of gaining an overall level of consistency.
"We will have to show we can do far better than we did in the game at Rugby Park."
Smith refused to be drawn on Jim Jefferies as a potential candidate for the vacant Scotland job but was more than happy to wax lyrical about his efforts as Kilmarnock boss.
He said: "Scottish football has not been in the best of condition financially for a lot of clubs for a number of years now.
"I think what he has achieved at Kilmarnock, keeping a team at the level they are at without having practically any money to spend at all, has been fantastic.
"I don't know whether I would have the enthusiasm to continue to do that year in year out.
"Jim has done that and, really, when you look at the turnover of players and the different aspects he has had to put up with over the period, it's been quite miraculous what he has done.
"Despite all the problems they have had, they have never really been involved in that many relegation scraps over the last few years.
"He does a terrific job for them."
Rangers 1/4, Draw 9/2, Kilmarnock 10/1