I love knitting lace very much but it did take me a while to learn. What I learned is no matter how confident you are use a lifeline!!!!
You can also break down the pattern and use stitch markers so you can have something to count to help you figure out where a mistake may have been made.
Starting off with a small project is a wonderful idea and remember, lace can be knit with any size yarn as long as the needles are way to big for the yarn so you can knit lace with worsted weight yarn, which make be more comfortable to start out with than lace weight yarn.
Good luck, you'll love knitting lace!