Do you have anything down in the rest of the cage? The litter box should be the only place with absorbent material, so if you have any bedding down in the rest of the cage remove it. You can add back a towel or fleece blanket later if you want, but for now just leave the bare plastic. I would also try moving the litter box to where she is peeing – if she’s not going in the box but is going consistently on the other side of the cage, just move it there. What kind of litter box is it? The corner ones are too small for most rabbits and sometimes they’ll pee elsewhere if they don’t like the small litter box. A rectangular one made for cats will work better.
She definitely needs exercise. You can put some old towels down in case she pees. Bunny pee isn’t hard to clean up if you get to it right away before it can sink into carpet – a 50/50 solution of water and white vinegar works the best.
As the others said, a spay can be done around 6 months.