First of all it won't be easy. You'll be competing against English, Australian and Kiwi- (amongst others) born lads who are just as motivated, but have been handling and kicking a rugby ball about since they were toddlers. Also -- are you playing League or Union with your Florida club? It makes a differences as opportunities in the League game (the variety played by the NRL) are a lot more limited than in the Union game, particularly in Europe. Even in America, the semi-pro League clubs (and even the USA Tomahawks) are dominated by expatriate Australians who qualify under the three year residency rule but aren't quite good enough to play in the NRL. Turning to Union (and Rugby USA) you'll need to excel at your club level, whereupon you'll catch the eye of one of the Division 1 or SuperLeague clubs. Excel at that level and you'll catch the eye of a scout for USA Rugby or one of the European clubs. They do pay some attention to the top-level North American teams. They other alternative is to attend school at one of the American colleges with a strong rugby program (U.C. Berkeley, Brigham Young, etc) and excel at that level. There're also watched by the USA Rugby and European clubs.
