Your transition ought to be smooth as glass. As you lower your carbine/rifle with your left hand, your right hand ought to have sidearm in it before your rifle quits moving- depending on the type of sling system you use.
What would be the chances of learning to be proficient with shooting your pistol left handed? The reason I ask is, lets say you're moving a stack down a hallway or any forward dynamic movement/formation- it's more difficult for a righty to cover to the right, where it would be natural for a lefty.
I hope your instructors have the insight to explore your situation to see it and shape it into a benefit instead of a mental roadblock. However, each dept is unique in it's training approach, and I hate to see you get too much counter intuitive info/habits here on the interwebs.
As for prepping- try to get as much productive range time in as possible, and learn as much as you can about basic formations and hand/arm signals.