How to make a cylinder-like base? (for a softie)

[camicami]

Hi guys! This is my first post in Craftster, I had to ask this before my head exploded from frustration.

I made this cat, really simple, just two pieces for the body and one for the bottom.
http://www.craftster.org/pictures/data/500/270599_10Sep11_IMG_4840.JPG

But the bottom completely stumped me! I have no idea how I should:

1- define the exact size the bottom should be; and
2- sew the actual rounded bottom to the body (with a sewing machine).

http://www.craftster.org/pictures/data/500/270599_10Sep11_IMG_4837.JPG

I made a mess on this softie because I was impatient. (never mind that awful closing gash, I knew this would be a throwaway practice piece so I didn't care about that)

So... please help?