I'm a 'no clip' proponent, too. I love that my birds can fly around. We make certain that there are fail safe precautions in place before they're even let out of their cages.
Is your baby weaned, or are you hand feeding her? Greys take awhile to wean. 16 weeks on the average is my understanding that most greys take before they wean themselves. I got my boy when he was 14 weeks old, and continued to syringe feed him until he was 17 weeks of age.
Congrats, and welcome to the forum! Looking forward to watching your baby grow!