If I were doing it, I would cut all the long sides and all the short sides to length from pine 1x3, and possibly an intermediate short piece to go about half way up the long length of the frame, depending on finished size of the frame. Then join the sides using biskets or dowels and waterproof glue. Buy a roll of screen, lay 2 frames on the floor long end to long end, put about 1 foot of blocking under 1 end of 1 of the abutted frames, staple screen to the distant end of the 2 frames. Remove the blocking and this will stretch the screen. Then staple the screen to the short sides of the abutted ends and then along the long sides. The cut the 2 screens apart. Screen moldings can be put over the staples for a more finished look and to prevent snags, then trim the screening around the outside of the molding with a nice sharp knife. Have the cat declawed! This is harder to explain than to do so let me know if you have any questions.