Whist you can trot a float with any rod, to get the best out of the experience there are two important factors; the length of the rod and the softness of the top. I would think a 1 1/2 lb b/s will be rather heavy for good float control, but you may get away with it. If the rod length will limit the length of the trot considerably, a few extra feet helps pick up a considerable amount of line, allowing for longer and longer trots.
I occasionally use my Avon rod (which has a b/s of 1 1/4 lb and is 12 ft) to trot a float under nearside tree cover and the like over short distances. But for long trotting I would want at least 13 ft if not more and a tip that has considerable give even when using strong lines. For this you can't beat a proper float rod. For barbel I use a 13 ft Tench float rod built on a GTi blank with 6 lb braid as the main line and a 5 lb mono hook link. A 15ft rod, such as the trotting special sold here would be even better. In open water, where there are fewer snags and you can let the fish run a little then a standard match rod may be OK. I caught many a barbel in the olden days on a 13ft match rod, with 4 lb line straight through to the float. However I wouldn't do it by choice these days; the fish are bigger and the snags worse on rivers like the Severn and fish care suffers with match tactics in that you often needed to play the fish to exhaustion.
With the rod you propose to use you will suffer from some missed bites, but if you do hit the bites you shouldn't have much difficulty landing the fish!
By the way, I can't think of a better piece on trotting for barbel than the recent piece written by Keith Spear that is on this site
here