Why pracę? And not pracy?
It's the accusative. Pracy would be genitive/dative/locative.
The model is in employment.
this was reported two months ago
I translated as female model and it wasn't accepted. I know it's not smooth but it isn't wrong?
We sometimes do accept it, so added here as well.
Yes, it is normal to say 'someone has work'- and it doesn't necessarily mean a one-off job and it might suggest short- time work, but it is still sensible. However, ye computer says 'No'...
"[The/A] model has work" works, it should have been accepted...
Is "modelka" the nominative case of the noun?
Yes. It's the female model. A male one is... well, just "model".
Could one use zawód here?
"zawód" = occupation, profession.