You could try that Fake lamb fur bed thingy. It might work. We have one for our dogs and they dig it and it is still as good as new, we got it at a dog show place so I am not sure if you could find one anywhere I know of. There are those similar ones that have the puffy rim around them but I don’t know it it would last for Mimzy.
(You know every time I think of Mimzy, I think of the poem, “Jabberwocky”
‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
“Beware the Jabberwock, my son!
The jaws that bite, the claws that catch!
Beware the Jubjub bird, and shun
The frumious Bandersnatch!”
He took his vorpal sword in hand:
Long time the manxome foe he sought—
So rested he by the Tumtum tree,
And stood awhile in thought.
And as in uffish thought he stood,
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!
One, two! One, two! and through and through
The vorpal blade went snicker-snack!
He left it dead, and with its head
He went galumphing back.
“And hast thou slain the Jabberwock?
Come to my arms, my beamish boy!
O frabjous day! Callooh! Callay!”
He chortled in his joy.
‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.)
That is what I think of when I think of Mimzy even though the Mimzy in the poem is spelt Mimsy.
Edit: There is a site that has these beds called palace pet beds, that could be a option. (It is the kind of bed our dogs have)