You will need:
- 3 long sticks/stakes
- wire or twine (to secure stakes)
- a bed sheet or tarp
- clothes pegs (to secure sheet)
Exactly the same way you built the tiny tipi you can build a tipi that you can fit inside!
Three big sticks. 
Some tent pegs in the making 
Making an X 
Wrap it with a sheet. 
Kitty approved 