What kind of fabric is it? Manufacturer? If it's a good quality quilting cotton (Moda, Kaufman, etc)with 1.5 yard pieces I don't worry about fraying too much, it's pretty minimal with pieces that size.
Another option would be to hand wash.
I can't remember the reason, and it may be one of those "old wifes tales", but I was told to never stay stich before laundering. That was ... more years ago than I care to remember.