Senior is 18 and under. If you turned 18 after August 31, you would be eligible to compete for one more season after that one. So yes, 2009-2010 would have been your last season to compete on a senior team.
Senior 5, you need to be 12 by August 31st of that year. Senior 1-4 and 5R, you must be 10 by August 31st.
Junior is 14 and under. You could turn 15 on September 1st and still be on a junior team for one last season.
Youth is 11 and under. If your sister turned 12 in June then she would be too old for a 2014-2015 youth team, but is age eligible for a senior 5 team.
Mini I believe is 9 and under but I am not 100% on that, and I have no clue without looking it up the age cap for Tiny.