Potty Problems ARGH

So, Harriet is nearly 10 months old, and we thought, housebroken. The last two mornings, however, the alarm goes off, we (Harriet and whoever drew the short, cold straw that morning) get out of bed to take her out (we don't have a fenced yard, so we have to actually take her out), she has gotten out of bed when we did, and went to the dining room and peed on the rug. We are literally 3 steps behind her. She does it so fast we don't see her do it. Does anyone have advice for me to stop this?

She's had urinary tract infections in the past, so we've had a rocky road to housebreaking, but she's not exhibiting any of the signs of one of those right now.

We clean that rug with enzyme cleaner, would it be a waste of my time to run a spot bot over it?

Frustrated!