The question doesn’t mean much if you're a digital journaler as you probably already have a synced copy available on your phone. But for the analog journalers out there this can mean mean the difference between having a journaling and having... lost our journal. Every single page of it.
There is no such thing as syncing and rarely any backup of our notebooks. So, carrying it everywhere we go is a real risk.
I don’t carry my journal with me because I know I will lose it. That's a scientific fact based on personal experiences (way too many of them) of losing a lot of things, from my keys and countless umbrellas, up to a brand new laptop (yeah, that's me, and would you believe it when I went back to get the laptop back it was not there anymore) as well as, you guessed it, my journal.
So, my journal stays at home.
What I do carry everywhere I go, outside as well as from one room to another in our apartment, is a pocket notebook of some sort and a pen where I quickly write stuff down. I don’t try to write great literature not even full sentences, it’s merely a few key words and symbols that have zero meaning to anyone but me and that work (wonders) as a reminder when I’m back at my desk and I write whatever I was thinking about when I jotted those down in that pocket notebook. And that small notebook, I don’t care much losing it.
For years, I used to get those free but real handy small notebooks with a tiny but decent ballpoint pen attached to it, from the pharmacy next street. It was their gift around New Year, knowing I quite enjoyed them, they would let me pick a bunch of them (not enough for a whole year but still, that was nice. This year, they gave me a... pencil pouch. It's an odd pharmacy, I suppose ;)