No,
You do not HAVE to join the union! How ever being unfamiliar with the industry, call your UA Pipefitters, Boilermakers or Ironworkers business agent (easy to find in the yellow pages). It could very well be a quick and easy "one stop shopping", and there is probably no better or higher respected training.
Also just for the heck of it, spend a little time with the search function in this site and there is plenty of advice and pointers for others with your same goals. The opportunities are endless
I personally don't agree with unions and would seek other avenues (I paid for my own training at a State Technical College and was able to pick up financial assistance and side work while in school), but, they (unions) have provided an "earn while you learn" for untold thousands of workers.
From my personal observations, Women statistically on the average make better welders than men. My last project, we had 2 women "brother-in-lawing" boiler tubes and chrome alloys (x-rayed pipe), never failed an NDE and made my QC surveilance easier than some of the intense monitoring that was necessary with many of their multi-chromosomed counterparts.
Do not let any negative stereotypes disuade you. Heck, I even taught my daughters to GTAW. In this day and age, law suits and safety rules have pretty much taken "the heavy lifting" out of most of the trades.
Go for it!
Best of luck to you.