Running

I'm going to be a FTM as of tonight or tomorrow (being induced at 41 weeks and 4 days). I guess this question might be more for existing moms and their advice. Would it be unrealistic to do a 5k road race six weeks postpartum (that would be on Thanksgiving Day). I'm a runner and I'm obviously rusty since being pregnant and I would of course consult my doctor first but I'm anxious to get back out there and I do this race every year....even if I half walk/run it. Thoughts?? Please be nice.