Here's a weird thing: in English (at least UK English which is where I'm from!) you don't use the present tense much to refer to something that's currently happening.
She goes to the market. (1)
Instead you use the present participle:
She's going to the market. (2)
The difference is that (2) means now, at this moment, she is going to the market. (1) you would use if she generally has a habit of going to the market, for example
She goes to the market every Wednesday.
In your particular case, personally I would vote for the past tense because the event of her leaving is in the past:
She's just gone to the market.
(italics mean the word is optional)