Update!
DD has peed 2 times in the potty and POOPED FOR THE FIRST TIME EVER in the potty this morning! I am super duper excited. She's 20 months and 1 day old today

I'm hoping to catch one more pee before her nap

Seriously, it's ridiculous how excited I am about this.
We switched to the bumpo potty seat thing that goes on the big commode -- I thought that the froggy potty on the floor would be better, since she could get off and on by herself, but she seems to like us putting her up on the big commode just fine (plus -- no cleaning poop out of the toddler potty!)
I bought her some 18m undies at target and washed them in hot hot and dried them for a long time and they shrunk up okay, with the goal that she can wear those when people are over (we had just been doing a sweater dress, but she climbs and there was still some flashing (it's a good thing the people who come over are family/close friends who love us).
Now, my conundrum is daycare tomorrow. She has just been in a diaper there (she goes from 8-12:30). Probably I shouldn't even mention going naked under her dress, should I? Sanitary reasons and all that. Her day care provider has 4 kids, all girls (actually 5 on Mondays). DD who is 20 months, the next oldest is 34 months, and then a four year old and a four and a half year old. (I'm not sure about the 5th who only comes on Monday, she's only been one week so far -- I think she's 2, but I'm not sure how many months.)
Her daycare provider said that she'd really rather wait until she was going on the big commode (and I can see not wanting to clean up the toddler potty). So, now she is going on the big commode, but she's been running around naked, too. Maybe I could put her in underwear after nap and see how that goes, and maybe leap in at daycare tomorrow with underwear -- I'm thinking that the 2 four-year-olds can help watch out for her grabbing at her vagina. It's kind of frustrating for me (and probably confusing to her) to make so much progress over the weekend and then to go back in diapers during the week).
Any advice would be appreciated. My friends IRL either have kids who are younger, or they waited longer (with more traditional signs of "readiness" -- DD is not very verbal) before starting.
Thanks!