Although Tyler ditched the high chair a little later (right before he turned 2), he wanted nothing to do with booster seats, small table and chairs, etc. He was perfectly happy to sit on his knees or bum at the grown up table. You might try a booster at the grown up table or a small table and chairs...just keep the receipt in case she isn't interested in either.
I'm a big fan of "start as you mean to go on" with this. I hate the idea of Tyler walking around eating, and our house rule is that all food is eaten at the table. Even at 19 mo, she should be able to understand that eating happens at the table, and when you get up, you're finished. We did that with Tyler from the start and it took a couple of weeks, but he got it. As soon as he'd get up, we'd say "you're getting up, you must be all done" and put the plate by the sink. If he sat back down a few min later to eat again, we'd give him the same plate of food and point out that he must be hungry since he's sitting back down at the table. He did a LOT of snacking and had no eating schedule while he got used to the freedom of being able to get up, but we were consistent and the novelty wore off and his meal schedule got back to normal. Now as soon as he starts to get up from the table, we give him a reminder by saying "eat more or all done?" so if he's really still hungry, he'll sit back down.
