I don't think its as easy as you make it sounds.
faking her death means she would have to lose contact with her father
(unless she explains to him that she basically had a 'bad dream'; no one will believe her) and how would a 12 yo find the means to fake her death?
and annulling the marriage seems to have major political backlash. it could be seen as going against the royal decree which is treason, and that's punishable by death.
Furthermore, she as the title of "pioneer" which means she's eligible for the throne, therefore, the royal family would want to keep her under their power to prevent her from competing for the throne.
So she can't just get pregnant for another noble especially when she's engaged to the prince this could also be seen as treason or worse! rebelling against the throne and trying to overthrow the royal family by making an alliance with other nobles.
the only stupid one here is that dumbass "god" for making such a stupid mistake with the one he claims to be "precious"
Basically, this isn't your average cute shoujo romantic fairytale, it has a lot of authentic situations and consequences
sorry for the long essay (⌒▽⌒)
tbh i reckon she's stupid. she's given a second chance at life and decides to do all this shit which is basically wasting her time. she could have faked her death or just confront the bitch and annul their engagement ( clearly in a nice way XD ) OR she could have just waited for the part where the PRINCES HOE shows up and annul it then or refuse the position the prince had given her i mean saying NO isn't fucking hard. OR WHEN THE BITCH SHOWS UP LET'S HAVE ARI GET PREGNANT TO ALLENDIS AND BOOM BITCH SHE AIN'T URS NO MOR there a fucking happy ending!!!!!
BITCH THIS IS HOW A MANGA IS MEANT TO BE WRITTEN