The ornamental design for a barbecuestand with shelfunit, as shown and described.
FIG. 1 is an upper perspective view of the barbecue stand with shelf unit showing my design;
FIG. 2 is a top plan view thereof;
FIG. 3 is a front elevation view thereof;
FIG. 4 is a back elevation view thereof;
FIG. 5 is a side elevation view thereof;
FIG. 6 is an opposite side elevation view thereof; and,
FIG. 7 is another upper perspective view thereof, showing alternate spacing between the barbecue stand with shelf unit, and a grill attachment and fire logs in broken lines.
The grill attachment and fire logs in FIG. 7 are shown in broken lines and form no part of the claimed design.