Translation:The girl does not eat tomatoes.
Is it incorrect to translate as "The girl is not eating tomatoes"?
Sounds perfectly fine to me.
Why not "The girl is not eating the tomatoes"?
Would I need something extra to indicate the 'the'?
That's fine, added.
If you really wanted to show it, you can interpret 'the' as 'these' (they often basically mean the same thing) and say "nie je tych pomidorów".