Okay, a few minutes...
First re: domperidone. It is available on prescription where you live, I believe.
I don't really think you need to take it, because you mention being engorged etc. It seems like you have milk in there, what we need to work on is getting that milk into Karrigan's tummy directly from your breast.
You say she is feeding for 5-10 mins. Great start. Is it active feeding like in the vidoe clips I posted? Because sometimes babies will hang out at the breast and not actually feed. You need to watch the clips to know what to look for. Good active swallows etc.
It can be hard to know what they are taking in, that's for sure. But bf is different...you don't count what goes in, you count what comes out. You are looking for 5-6 good wet diapers (disposable ones). It should be as wet as if you poured 3 tablespoons of water into it, that's how heavy it should feel. And then about 3 poopies.
What I would do, is just take a day, put her directly on your breast as often as she is cueing, drop the supplements. Of course, you need to ensure you have a good latch, hopefully your lc will help you with that IRL. Feed feed feed, take a look at your diaper count and see where you stand. It is possible she may need supplements for awhile, but this is a good way to get a baseline and see where you are at with it.
I just want to say quickly, as I hear Kate stirring, that I commend you for trying this when it didn't work out last time. Like I said, I had multiple issues starting off with Kate that I didn't expect after nursing Riley for over a year. It was so hard to keep going some days with pumping, trying to latch a crying baby etc etc all with a toddler running around. I drew on my experience with Riley to keep me going, I can imagine it's all the more difficult for you as you didn't have that positive experience first time round.
These next few days and early weeks may be a trial, I think it is for most with nursing even if you are not having major issues. But chin up and plod ahead. We are with you every step of the way!