Personally I'd allow 45 minutes to an hour, though it will probably be faster than that, more like 30 minutes. Your actual driving time is more like 10 minutes.
The parking lot at AK is large, and if you're not near the front you'd be waiting for the tram to get you to the front gate area, where you must go through security and the ticket turnstyles, then walk about 15 minutes to the Africa area where Tusker House is. I'd rather have the extra time figured into my schedule than be running through the turnstyles and pushing everyone to hurry up, puts me in a better frame of mind to enjoy breakfast.