I have a 3lb poodle(5 yrs. old) He was also very small (1 lb) when I got him, I bought a small carrier like shown in other posts. I put a piece of lambs wool in the bottom so he wouldn't slide, I also put a soft small purse in with him as my purse therebyby only having to carry one bag, also some of the bags have pockets on the outside and you can put your wallet and keys in the pockets, worked great for me!
Charlie's mom (Arlo's and Alfies and Bosleys mom too)