If you can wait, the Pet Journal cap will be removed completely in upcoming Patch 9.1. This means you'll be able to collect and add as many pets as you want (still only up to 3 per non-unique pet).
It's unknown when Patch 9.1 will be released though, so it could be a while before you have a larger journal size.
If you absolutely cannot wait and need to add pets to your Pet Journal now, there are 2 items that will increase your journal size to hold 1500 and 2000 pets. I recommend not even bothering with trying to get the 2k upgrade, because of the Patch 9.1 change. If you're desperate for Pet Journal space, the 1500 upgrade (
Pocket Pet Portal) should be good enough.
Again, if you can wait, I recommend waiting for the next major content patch. You'll get a free Pet Journal upgrade, and you won't have to spend Polished Pet Charms on the Pocket Pet Portal, which is a plus. But downside is you'll have to hold onto any pets, or hold off on collecting pets, that will put you over the current journal cap until 9.1 is released. Ultimately, it's up to you, GL!