Keith Urban's not letting his personal life get in the way of his professional ... hopping back onstage for the first time since Nicole Kidman filed for divorce. Urban reportedly reflected on his own beginnings, recalling how his parents supported his dream by allowing him to leave school and chase music full-time. It's unclear if Maggie Baugh performed with him ... remember, she's the musician who he changed the lyrics of "The Fighter" for back in April -- singing to her instead of about his now-estranged wife Nicole. We broke the story ... Keith and Nicole separated earlier this year and lived apart all summer -- with our sources saying it was entirely Keith's idea, and Nicole didn't want to split. We got exclusive photos of Nicole flying under the radar in Tennessee Thursday after a rough week but she couldn't escape the camera lens of the paparazzi.