if i just put bedding in the liner it should be fine yes?
No. Bunny will still chew the liner. Bedding won't cover the sides of the liner and bunny can dig any bedding away to get to the liner on the floor.
The cage is also too small. Have you had the time to look at the two links provided earlier? I think it would be helpful to see a number of other cage options that are shown on those links.
Also, remember that rabbits potty train which makes cleanup much easier. When a rabbit is potty trained, they do not (should not) have bedding all over the cage floor. That just makes a mess, is a pain to clean up, and is costly.
The second link (to my website) has much information on how to prepare for a rabbit
before you get one. The mobile version isn't as user friendly as a desktop/laptop version. Rabbits are unique pets and many of us, before we got a rabbit, didn't appreciate just how different they are. The more one can learn about them beforehand, the better it is-- not only for the person but for the rabbit as well. Here are other relevant links that should be worth the time to check out:
https://rabbitsindoors.weebly.com/myths.htmlhttps://rabbitsindoors.weebly.com/choosing-your-first-bunny.html
As for having carpet on the floor, that shouldn't be a problem. There are several options depending on the type of cage or pen you use. Linoleum/vinyl flooring piece is an easy to clean option and can be seen at some of those links. The key is to be sure bunny cannot access the edges. The photos show how this is done.
Height isn't a concern if you make a cube grid cage since it can have a ceiling. If you use an ex-pen or similar, I would not go less than 30" in height. With pens, it's important to not have hidey boxes placed near the pen wall otherwise bunny might use it as a step to jump over the pen.