Duplicating History to get a free skill proficiency choice? RAI, no; RAW, no
When class and background skills overlap, you can just pick whatever; from the PHB, pg. 126:
If a character would gain the same proficiency from two different sources, he or she can choose a different proficiency of the same kind (skill or tool) instead.
This quote is in the context of backgrounds, so it's uncertain as to whether this reasoning would still hold in this context.
On one hand, even though this quote is in the context of backgrounds, the class and the Domain are still two different sources, and since this is all happening at level 1, a strict out-of-context reading of this rule suggests you can just swap out the duplicate for any other skill.
On the other hand, as suggested by @Theik, "if you follow that line of reasoning, you can do weird stuff like pick perception from your class if you're an elf, and then because you now have perception from two different sources decide to pick any other skill, instead of being able to pick from any other skill from your class list. The backgrounds are flexible, the class skills are not."
However, since this is still during level 1 character creation, just don't pick History from class, then there are no overlaps; otherwise this would essentially be a wasted skill. Since this was an attempt to get a different skill, the player will have to find another way to get that skill (being an elf, half-elf or variant human, taking a feat like Skilled, etc, there are ways without sacrificing her background skill choices).
It at least seems to be against RAI (Rules As Intended) and is likely against RAW as well, given that the quoted rule was presented in the context of background and was likely intended only to apply there.
In fact, Jeremy Crawford has said that this quote is only for backgrounds, which backs up that this is not RAW or RAI (thanks to @V2Blast):
The proficiency rule for backgrounds applies when you gain your background at 1st level. It has no relevance outside that context.