I don't think that would be comfortable. Personally, I'm a fan of these two:
International Pup Carrier - Dog.com Celltei Basic Pet-on-the-Go, Messenger Bag Style Pet Carrier
You can get a discount for Celltei bags here:
Customer Appreciation discount coupon from Celltei
There's also a page for buying some at reduced prices:
SPECIAL
Several people here like the Fundle pet sling.