Maybe start running with her? You might need to wait until she is just a little older before you put her in a jogging stroller though. If you make a goal like run a 5k in 3 months or 6 months, it really helps get you motivated. If you don't run, couch to 5k works great to get you started. You can also do that with her, and it doesn't have to be early. If you really want to go to the gym, is there daycare there? I go to our local rec center, and my son just goes to the day care there (and has since he was around 6 months). Again, so it isn't so early, and if you enjoy it, it will be enough motivation.
One other really motivating thing, exercise with a friend. If you are both getting up at 6 to do something together, you can't let each other down. Sometimes that is the only way I get up and run or workout, can't let my friend down.