Whenever you are glueing glass you must consider the visibility of the adhesive. If the glass is translucent, you will want a glue that dries as clear as possible. Before glueing any glass bond be sure that the glass is clean, free of any oil (even from your fingers) and dry.
When using dowels, select a size half the thickness of the wood being joined. For example, for 3/4-in. stock, consider 3/8-in. dowels.; for 7/8-in. stock use 7/16-in. dowels. The length inserted should generally be three times its thickness. Thus, a 3/8-in. dowel should be about 2-1/2 in. long to penetrate into each member 1-1/4 in.