Big Dursts are just that, BIG. I have a Laborator 138.

If you are pondering a trolley, then figure out how low it will have to be to get the top of the column through any doors. Do you really want a trolley that low to work off of?
Will the trolley have enough mass to not be top heavy?
Are sandbags placed on a lower shelf to lower the centre of gravity going to be needed?
Most certainly you will need to lower the head all of the way to even think of moving it.

I would plan to make a cart have 'drop wing's' to make the top surface wider once set up than would otherwise be possible while tucking it away to store it.
A place is always needed to store focus finders, sit a timer, dust brush, negatives filing binder, test print rig, contact printers, paper trimmer, etc.
A shelf just under the exposing surface is a great place to tuck everything away when moving it.
An even better option here would be a light tight drawer so that enlarging paper, perhaps to 16x20" size could be put while out of its outer packaging.
The drawer could double as storagelocation for top surface items when the cart is wheeled away.

If the makeshift nature of your location allows you to devise a way to 'clip' the trolley to the wall,and then have a means to also anchor the top of the column to the wall, that would go a long way to help to align the thing and make it more stable.

I see your 3cm thick solution wood being mounted to 100mm square post 'legs' that the outer skin panesl could be lagg bolted onto.
Some quantity of angle steel plate may be used to attach the wall bracket to the trolley. I don;t think wood alone will be strong enough unless it is a piece of hardwood.

I see that the 60cm wide wood you are considering might be the limit of the width of the trolley.
That is not wide enouigh to do justice to the capabilities of this machine.
I would recommend a baseboard at least 90cm wide to accomodate a 11x14" four bladed easel easily, and accomodate the occassional 16x20" or 20x24" sized prints held in impromtu easels.

I know the advice that floats around here is to buy the biggest enlarger you think you will ever use, and you certainly took that advice to heart with your first enlarger buy.