hello babybabybabybaby (love the name!)
I've had an underactive thyroid since I was 14. (now aged 33 going on 17). As long as you are on the right dose, you should have no more problems getting pregnant than anyone else. But make sure they test it every so often, as it does take a while to get the dose right. if you feel tired, and feel that your hair and skin are getting a bit 'bla', or if you have a bit of a goitre (that horrible lump in your neck) that's an indication you should ahve a blood test to check the levels again.
Also, they say that your dose might change when you're pregnant so the mw will probably take blood tests for that every now and again, and you may be referred to a consultant just as a precaution - this is nothing to worry about! mine was fine all the way through my pregnancy, but when DD was about 9 months old, I had to have my dose increased and I'm back to normal again now (DD now 22 months).
the only horror story I heard was that it might make constipation worse when you're pregnant, but a) I can't see how it could be worse, and b) if the dose is right, you shouldn't be any different from anyone else, so I think that tale is a load of baloney!
if you HAVE to have something, this condition isn't too bad, as long as you keep taking the tablets!
don't know much about low progesterone but hopefully you feel better about the thyroid issue now! you'd be surprised how many people have it!
Good luck!