i would suggest running a sponge filter in the established tank for about a week's time and also as you add that dirty sponge to the new tank you can take some of the the filter material from the established tank and squeeze it into the new filter or you could be like me and run the new filter on the established tank for a while before you set up the new tank.
As far as the tank on the dresser, the overhang on the 2 sides may cause undue stress on the bottom of the tank and it is important to have support along all the edges of the tank.

__________________