I have a character in a fantasy story who wears a strong leather armor that covers her entire body. Would this be practical?

Without enough details… sort of. Boiled leather plates make for some marginally decent, if not very sturdy, armor. The plates aren’t particularly flexible, which is why you can use them as armor in the first place.

Properly treated leather isn’t as good for armor, but you can make an outfit out of it. It’s probably not going to be extremely comfortable without other materials getting used in the process, but yes, you can wear it.

You could combine the two to get a full body leather outfit, though you’d probably want separate pieces forming the jerkin (shirt), pants, boots and gloves (or full guantlets). If the chest includes a hood or if there’s a separate helmet would be up to you.

To be clear, I’m talking about an outfit, not a single piece of armor that covers your character’s entire body. A one-piece body suit isn’t going to be practical. This isn’t just a combat concern, by the way, it would also be an issue if your character simply needed to go to the bathroom.

We’re also talking about armor that isn’t going to be as good as metal. Boiled Leather is better than going out there with nothing but flax padding between you and an axe, but it isn’t a huge improvement.

It doesn’t really matter if the plates are exposed, visibly stitched onto the jerkin, or if they’re under the surface as part of the insulation, like a modern motorcycle jacket. I slightly prefer mixing it with the insulation, because that prevents your character’s foes from seeing the weak points in her armor, but at least in your writing, this is probably more of an aesthetic choice.

In general, full leather like this would work better in a colder environment. In a hot environment, you’ll perspire everywhere and be miserable.

Now, given it is a fantasy setting it’s possible the boiled leather is something mystical or exotic, like, say, manticore hide, and hard as steel. But that would be an aspect of world building you’d need to decide on and not a question about historically available armors.