sweeney todd is set in victorian england, circa 1846 (at least that's when the original story of Sweeney Todd was published)
so, yes, Beadle would be wearing the shirt with the oversized collars, vest, frock coat, etc of that period...
here's a better picture of what he wore:

canes were pretty popular at that time (although I believe they called them walking sticks then) - lot of were topped with figures of imaginary beasts...some even had stiletto blades inside....(think Lucius Malfoy's wand/cane in the Harry Potter movies)
this is the only picture that I can find that shows some detail of Beadle's cane: