[reuelt]

Send the 1-1/2" pine thru a 13" thicknesser (AKA Planer in USA) reduce to 1-1/4" square (can do 8 sticks at a time together)
Then 5/8" radius round over router bit (4 times on router table) would give a nice 1.25 diameter round rod

 

[reuelt]

U

Exact radius round over bits won't give a smooth cylinder. The guide bearing will be riding on a curve for at least two of the passes and give a noticeable offset. 1.5" square stock is best rounded with a 5/8" diameter bit and the rest can be done on the lathe.

Remember the router table has a fence.
So it is possible to get a smooth cylinder if we start with a smooth square.rod.
We can also use a 5/8" Half round router bit instead.
(manual wood lathe would be slower but GUIDED copy lathe or CNC Lathe will be OK)