They don't give a gauge for this pattern
That's a problem if you want to use a different yarn. Funny thing is, they even say if you want to use a different yarn, make sure it's closest to the gauge for your pattern.
Ugh.. silly pattern writers.
That said, the gauge for the recommended yarn (Trendsetter Blossom) is 3.5-4 sts per inch on size 10 needles. Look at the gauge for the yarn you are using, and try to equal that 3.5-4 sts per inch. Use a needle size one size smaller to start your shrug, since their pattern starts on size 9s. Then switch to 2 sizes larger when they switch to the 10 1/2s.
That's the best I can recommend. If there was a pattern gauge, not just a yarn gauge, it would be more accurate.