Hi jillandbellabunny
Welcome to the forum. : )
It sounds like a good plan and you will find the clean up so much easier on you! That litterbox looks great. Rabbits can lift tail high to pee so the higher sides help keep things contained. A bigger box is usually better for successful litter training. The one in the link appears to be a decent size and should work well.

You could get 2 initially while training, if you want. Then get it back to one in the cage and use the 2nd out in the house for out of cage time. A bonded pair shouldn’t have a problem using the one box though, if you just want to get one to start with.

I’d actually introduce it in their current cage and lay something over the top of the wire flooring, before transitioning to a new cage. That way, the litter box will be familiar and hopefully they’ll continue to use it once you set them up in new habitat.  Rabbits can have tendency to mark new spaces with pee and poop initially. 

p.s.: I made small edit to your post to make the link clickable.  

I have three bunnies, and they have two litter boxes, inside a bigger box with hay in between the two

As long as there’s enough space for both to easily fit in the box, one will be fine, but I think generally advice is one each.

You didn’t ask about what to fill it with, but there’s lots of options so thought it might be helpful to mention!

You can use non-clumping pine pellets, which are often sold as cat litter, or stove pellets I believe.

You can also use a paper based litter like Yesterday’s news or Back2Nature, which is what I use.

Some people use hay, but it isn’t especially absorbant and can end up staining their feet  

Don’t use clumping cat litter, as it can cause a blockage if they ingest it  Also wood shavings are bad for bunnies, and also make a huge mess for you!