YOu did a good job lunging if that is your first time doing that with her.
Couple of things;
Be careful not to be holding the lungeline in loops, in case horse pulls really hard and you get caught in a tightening loop.
Pay attention to how you use the whip, so that you are not kind of "nagging" at her. So, when she is going correctly, you keep the tip lowered and quiet. Only if she slows or breaks gait, or ignores a quiet "ask" do you increase the pressure from the whip, then as soon as you get it, put that whip right back in nuetral. I saw too much waving of it up and down, kind of meaninglessly.
Hold the lunge line just as you hold the rein in English style riding. You can tighten your hold on it (by firming up your hand and forearm) and even exhale and lower your body to assist in downward transitions, and preperations (like a half halt) for an upward transition, where in you raise up, inhale and open you hand slightly and ask her forward with voice, almost immediately backed up with whip.
When you lunge, imagine yourself riding, hold the line like the rein, and your body as if you are in the saddle.