I set out today in search of some teepee materials, here's what I found at Ikea:
Black + white sticks ($4.99) and mesh curtains ($4.99).

I was hoping that I could double up the thin sticks in the package to make longer sticks but they were just too thin. It came with 3 thicker sticks so I decided to just make a mini teepee that would be a perfect baby size. It's still a little lightweight. I'll have to search for some bamboo sticks that are heavier to make a real teepee that my daughter can actually play in!

I put a rubber band around the top of all three sticks and then covered it with jute.
Then I cut a section of one curtain panel and draped it around the teepee structure and secured with more jute at the top. I also cut little slits in the mesh so I could tie back the opening to the sticks.