Do you have someone who can watch your daughter? It might be good for you to get out on a Friday night.
If you meet her half way, it's about a half hour drive if I'm reading this correctly. Will you daughter sleep in the car on your way there? On the way back?
I travelled a lot from the time my kids were very young, infants, and they were well seasoned little travelers. For instance, my son's first long distance trip was at 3 weeks after my beloved mother in law passed away unexpectedly. My husband took off without even packing anything after I got the phone call that she had collapsed. He was a little more than half way there when he got the call that she had passed away.
I packed for my husband, myself, and two kids and set off.
My kids just adapted to life around us as opposed to the other way around.
You know your child better than anyone so do what's comfortable for you, but a night in the city with a dear friend sounds pretty awesome to me.
I hope you get it worked out.
Best wishes.