#There is no difference which hand you attack with first in general

There is no distinction between main and off-hand in 5e unlike in previous editions. Thus, attacking with either left or right hand first does not matter. 

With different weapons in each hand it *could* matter, but only in the case where one weapon offers a higher ability bonus to add to the attack. In that case, you would want to use that hand/weapon first.

In your case specifically, it doesn't matter because both are finesse and thus it doesn't matter which one you add your Dex/Str bonus to, it will be the same. Thus, she could absolutely attack with her left hand dagger first, doing 1d4 + Str/Dex mod damage, then attack with her right hand shortsword, doing 1d6 damage.