Hi Jessica and Welcome! Congrats on your baby, that is so awesome you got your bfp before needing the ivf!
I used this calculator:
Pregnancy Due Date Calculator | Tools | BabyCenter
and put in your O date, so it has your EDD at December 26. So, May 4th you should be give or take six weeks. You will probably be able to see something on the ultrasound, but the heartbeat may not be visible yet...I'm not sure, my first doctor wouldn't look until nine weeks, but they had really old crappy equipment at that hospital, so yours might be better.
As for the O date, don't bother trying to tell the doctor's office that the lmp date is wrong, they use it no matter what you say. They'll measure on the ultrasound and give you a new date anyway. I kept trying to argue about my dates, but they didn't want to listen. Now she is measuring within 3 days of my O date, so they'll get close eventually. Babies never come on their due date anyway, or so I hear.
I hope you have a great appointment in a few weeks!