My Lila was only 3lbs 3oz (she is now up to 3lbs 8, yay!) when I had her spayed and I swear, I was just as worried as you! (I actually told every customer that came into the restaurant I work at to pray for my "baby" because she was having surgery that day, lol!) But Lila did beautifully and the recovery was a snap!
And for the record, I don't think you waiting makes you a bad mother at all! I think it makes you just as paranoid and overprotective as the rest of us crazy YT'ers!