Not quite. The word coat is masculine and therefore the colour has to be adjusted to the masculine noun that is discribes.
If it would be a blue table it would be the female version as table is female in Arabic (and in French by the way while Table is male in German)
عند means at or by. Therefore, like how in English you don't say "Judy she has...", in Arabic you don't need to say "عندها جودي...". Do note, however, that in dialect and less formal MSA, the common structure would be "جودي عندها..."