Vet bed is excellent stuff, it is easy to wash, quick to dry, lasts for years. Wash with bio laundry stuff of course. Also, wipe out the tray of the crate with something like Simple Solution hard surface cleaner to remove all odours which make your little one more likely to pick that spot again. You want to have a couple of pieces of vetbed, one in the crate and one in the wash, usual arrangement.
As has been said, using the crate as timeout is not a good idea. It needs to be your pups special place with only good associations. You should be feeding him in there, and hiding little treats/toys in there for him to discover. It should never be used for punishment/timeout.
You say that you don't understand, at night he whines to go out and when you take him out he does his toilet. I am not clear what is wrong here?
I am also not clear why you are considering taking away his bed.
Your pup will not willingly soil his bed. But he is only little, and cannot physically hang on for long. Watch the body language, there will always be a signal that he needs to go - the nose goes down and briefly sniffs the ground, and then you need to act very quickly, you have just seconds to pick him up and take him outside. Then lots of praise when he toilets, and use your cue word too of course.