ASA/USA Softball you HAVE to qualify for the most part and so there will be travel to qualifiers to get in, but as you are in the South this would be the 'target' event for the top teams in the area.
USA Elite - while you technically have to qualify, there is some more leeway if you perform decently in these qualifiers. It would be the fall back event.
PGF is your other real option - if you want the very best and don't mind going to California there will be some PGF qualifiers in the South/Southeast. But we are talking really expensive and for a non-West team I'd be saving that trip until 14-A or even 16-A. And there will be limited qualifiers in your area so you will REALLY have to be at the top of the list of teams in the age group.
And if you don't get into these then USFA (panama City) or USSSA (Viera/Orlando at the new complex) have been much more competitive and balanced the last few years especially in the 12U and 14U age groups so are also excellent fallbacks.
.. Lastly, don't spend $$$$$ on chasing qualification in 12U. It is really expensive, the travel is really expensive and the kids get burnt out (though they will tell you they are not because they are 11 years old). The amount of highly talented girls who leave the sport because of heavy 10U/12U travel schedules is extremely high. If you can qualify early for your target event or are just chasing competition, play up in the older age groups locally versus chasing same age competition. Long term it is a better path and will help keep the girls in the game.
The 12U ASA Champion from about 4 years ago were based about 10 miles from my house. Of those 14 girls, just 1 plays softball today. Just something to think about.
There is more leeway in the ASA qualifications than USAES. We qualified for both and ASA was definitely the easiest giving 3 berths for a 12 team open tournament. USAES 2 weeks ago had a qualifier with 27 teams in it I believe, they gave 2 berths (all A teams with at least 5 different states represented).
I would definitely stay away from Sparkler and Fireworks, it's jus a big money grab. Yes colleges do attend but look at the number of teams/players and work the numbers. Most kids are never actually in front of a college.
I agree with marriard, if you want competition, go up in age and stay local as much as possible. You start beating the top teams in A class the age above you then start searching for better competition. No matter which tournament series you go after, you will have to beat a team that is probably good enough to beat your older local competition. At 12u keep it fun some, the USFA in PC that JAD mentioned sound fun. Maybe do both if possible.