I did something similar with my daughter when she was 21 months old. I just bought about 20 pairs of underwear, gave her lots of water and hunkered down for a couple days. When we went out, I took her portable potty with us. It was the kind with three parts... a base (that doubles as a stool), a seat (that can also be placed on the toilet) and a reservoir. I had her go pee before we went into any store. We only had a couple accidents while we were out. It actually took a few weeks before she was trained to pee on the potty. Now BMs on the potty were a different story. That took a couple months, but we had plenty of underwear so we just threw them out if she had an accident.
The biggest thing to remember, no matter what potty training method you use, is praise, praise, praise and never scold. We didn't ever use stickers or M&Ms as a prize... we just sang and danced and acted silly whenever she used the toilet.
Best of luck!