First off going as a Jr. can be tough.
But, you are so involved with what you are doing and that is also so important for not only You but the School.
While it sounds like you would be in said Sorority for a short time, you could and would be an asset to them to show what Our Sisters do!
Go for it. If they do not take you, it is their lose, not yours.
But nothing but the very best for and to you!!!!!