units in any column of route always formed into column of division prior to deployment, the division being whatever the appropriate tactical sub-unit was for the particular nation, battalion organization and drill manual in use. Deploying on the head is well covered in all the period manuals. You now have Torrens electronically and should find what you need there as a good example. I bet Google has trashed the plates, but the text should come clear with enough reading and questions of the sort you are raising.
However, you will find that a brigade on the march rarely deployed on the head. The first thing to understand is that the brigade would be marching in battle order, either by the left or by the right. The default was by the right unless specifically ordered to march by the left. Assuming the brigade is marching in column of march by the right, then the right hand battalion is leading, so all other battalions would normally fall in to the left in succession as they came up.
The first technique to convert from the march column into line of battle involved the column making a right wheel and then proceeding sufficiently far that all battalions were clear of the approach route (or had advanced to a place designated by a superior general - remember that most brigades approaching a battlefield were part of a larger army). Once in location, the brigade would halt and wheel up into line. Don't forget that line the case of a brigade or higher means that the battalions are in a line, not necessarily that each battalion is in line. In Frederick's day, the battalions would form open column of companies as they marched. When the column halted, the battalions would wheel up into line. Have a look at Leuthen for a very elegant example of how the approach march on a carefully selected angle could have a devastating effect. By 1815, it was just as likely that the battalions would exit the road (assuming they were in a march column suited to the road width), form open column of division on the march, then close up to whatever distance that nation used for tactical columns (half distance for some, quarter distance for British and closed column for others). The battalions would probably maintain full deployment distance from each other. When the brigade was in position, the battalions in their column would wheel towards the enemy.
Note that if the brigade was marching by the right, then it would normally wheel to the right to leave the road, then each battalion would wheel to the left when the brigade fronted the enemy.
The second technique involved the lead battalion halting and the following battalions forming line on the lead battalion. At the simplest, the lead battalion halted in place, then each successive battalion fell in to its left (assuming the brigade is marching by the right). There were two principal variations. The lead battalion could oblique to its right to ensure that the brigade was centered on the road or some other designated point. Or, the column could halt and form on a middle battalion by having the lead battalions retire obliquely to the right of the designated battalion and the rear battalions oblique to the left of the designated battalion.
The above assumes that the order of the battalions within the brigade was important, which was generally the case. Whenever commanders had the time and space to properly deploy their lines they would, since this was the formation in which the units were rehearsed. If in a rush, or if it was a meeting engagement, battalions would be inserted where they were most needed as they came up. Compare the manner in which the French army deployed onto the field at Waterloo to how Davout committed his forces at Auerstadt to see the difference.
Now as far as the battalions coming south from Brussels to Quatre Bras, they would almost certainly not be in fours. The chausees were LARGE roads with a paved centre and broad shoulders. Look up chausee in the archives, especially posts on the subject by Bruno Nackaerts for descriptions of just how broad.