19 months is a time for safe exploration and a lot of discipline. This is the time for them to learn that it's not OK to play in the toilet, pull things off of the shelves, open up drawers etc. In order to help with these things you need to set clear expectations but she will test these boundaries often. I know you are mostly interested in the learning aspect of things. But trust me when I say that obedience must come first. It's impossible to really teach a preschooler that never learned to sit still, listen and obey. You say she can't sit still long. Of course, she can't be expected to have a long attention span. But it will be up to you to teach her that. So I suggest pulling her into your lap as often as possible and looking at books together. Keep a watch or clock nearby and try to always stretch the sessions just a little bit longer. Do the same thing with anything you do. If you are stacking blocks keep track of how long. And by all means now is the time to teach her to put her toys back. Whatever she pulls out of a toy box she puts back. Also teach her to put back the toys she is playing with before she moves onto another activity. I know it's hard to teach and a lot faster and more efficient to just do it yourself. But that's not going to teach her.
It's good to provide them with a safe and good way to do some of the things they really want to do. You can create a sensory table or little dish pan where she can play with shaving cream, soapy bubbles, finger paint etc. If you have book shelves (and of course have them bolted to the wall), give her a shelf and teach her that one and only shelf is hers to keep her own stuff on. Then she has one shelf she can pull things off of. But then she has to learn to put them back too.
I've had a lot of kids at her age that could learn some letters, most of their colors and simple counting. But I really believe that the most important thing you can do at this stage of the game is to work on creating routines in your life with her for instance, never have a snack or eat a meal without picking up any toys laying around the house first. It's not a scheduled activity necessarily. You may not always have your snacks and meals at set times. But once you set the rule of cleaning up first it becomes something your daughter can count on. It's just like learning to wash hands before meals and where she's allowed to drink etc. Now would be the time to teach her she only eats and drinks in the appointed place and that food and drinks shouldn't be carried around the house. Hopefully, you never started that.
You can turn everyday chores into teaching. When setting the table, count the plates, cups, spoons etc. Ask her what these items are and then you are working on vocabulary and talking.
When you are doing laundry put a few socks in front of her and have her help you sort them out. If some of them are colored talk about the colors.
The attention span concept is a bit of a pet peeve with me. Running a daycare as I do I get a lot of time to play with the ideas. I've always heard you can count on 5 minutes per year of life. So following that line of reasoning you can count on 5 minutes and no more for any activity. But I've stretched these limits quite far with most of my kids.
One way I work on that is by setting times where I want to read or need to do something that ordinarily I'd need to do when the kids were asleep. So I'll have them wherever I am and I'll put out a rug or blanket and a set of blocks, box of toys, books etc.. I'll require them to stay on the rug while I do whatever it is. I'll tell them going into it what I need to get done and how long they will be there. When they get up they get put back. Once they learn that they will play right there during that time they turn their attention to occupying themselves. At 19 months it is a real chore to teach them to stay. But by just over 2 my kiddos can occupy themselves for 30 minutes at least. Once they can do that then they can sit at the table and draw or play with building blocks for a reasonable period of time.
One reason I'm such a stickler on this is because as a teacher with several kids, it's annoying to spend more time setting up an activity than the actual time the kids spend on an activity. Before I realized how important this was I'd spend 20 minutes setting up an activity for them to get bored and want to move on 5 minutes into it. Then they are playing freely while I'm cleaning up which may take another 10 minutes. So I've invested 30 minutes into something that only lasted 5 minutes. Ummm NO. That's not efficient use of my time and it's certainly not efficient use of a Kindergarten teachers time.
As a daycare provider I consider it my highest priority to deliver happy, intelligent, obedient and compliant kids into the hands of the degreed professionals. They should not be wasting their teaching time in school dealing with kids that were not taught properly at home and daycare.
I hope some or any of this helps :)
Suzi