Clear perspex 'rod' / dowel 5mm dia (Malvern Link WR14)

Hi I am repairing a friends tea towel rack which is made of clear perspex, 1 of the knobs has broken off, it cant just be glued as there will be no strength. As the knob is hollow and there is a recess in the main part of the rack I am hoping to insert a bit of clear perspex rod/ dowel and glue it in place. Size required is 5mm dia, preferably needs to be solid not hollow and I only need a couple of inches in length. Thanks