Yes I think it's normal too, and I think it's normal for you to start feeling irritated by it lol.
My dd is 22mo and about a month ago, I reached my limit and decided that I would try to substitute a drink of water and a snuggle for nursing during the night. I explained to her that there wouldn't be any booboo while it was dark out, that booboos were sleeping, just like she was to be sleeping, so when the sun came out, she can have booboos again. The sun comes up at 5:30am but that is totally acceptable to me. She still wakes up once or twice a night, then does a marathon nurse from around 5:30 or whatever until about 7:30 when she wakes for the day (I sleep in her bed with her at some point during the night so I doze in and out as she latches on and off in those early morning hours).
I was shocked at how easily she accepted the snuggle and drink of water as a substitute for her booboos. The great thing is now that dh can easily get her back to sleep, as can anyone else, like my MIL so dh and I can go on dates
She even knows now, when she wakes up at night, as soon as someone goes into her she says "Water. Hug."
My first was the same and we nightweaned at 22mo. He also easily accepted snuggles from daddy, I slept on the couch for a week. No tears were shed.