So I get what you are saying but at 3rd level I would not let her character live. If the party is wealthy enough and inclined enough they can take her to a city and raise dead. Otherwise let her roll up a new one and join at the party's level. Focus on the opportunity to try something different.While DMing today, a PC died today, 2nd level on the cusp of 3rd. It was partially good DM rolls, partially poor planning. The battle:The PCs attacked a xvart lair then left to take a 1 hour short rest. Xvarts aren't stupid, and they regrouped the bulk of their forces in a central war room while directing a force to trail the PCs and block any escape. Rather than infiltrating the lair and taking it room-by-room, 5 2nd level PCs faced a very deadly encounter of 13 alert xvarts, 1 xvart warlock, and 1 giant tick. Given the PCs had killed a sacred whiptail centipede, destroyed the centipede hatchery, and insulted their deity, this wasn't a battle where prisoners were going to be taken. It wasn't a glorious death that anyone will write stories about.
I generally don't like pulling punches in my games and roll in full view. In doing so, I can't fudge away a character death when the dice do their thing. I'm not inclined to because if players catch on the DM is going to intervene every time death is near with a convenient plot device, it'll cheapen the experience. After all, why roll in combat when you know the DM won't really let you perish, perhaps because you wrote an awesome backstory that fits with the campaign?
Still, it stinks. I can tell she was bummed, and there's not many options for low-level characters. A few weeks ago, I pulled a DM intervention for another gamer whose character died at 1st level due to a really unfortunate random encounter roll. Thanks to befriending some fey, they quested and got hooked up with a druid reincarnate, and a hefty IOU. It was good times and in the past I've turned low-level death into a quest.
Should I intervene, again, though, with another convenient story plot device given I just did so? I've got ideas, but it feels contrived to do this twice in a row and so quickly.
I knew a 14 year old girl that went into a full blown week long depression when her 15th level 1E character was killed for good in a TPK. In her defense she had been playing it for well over a year.
With a first level character it is a bit different. I would never have wandering monsters in a 1st level game. Characters are so vulnerable at 1st level that that could die in any fight. For 1st level characters I prepare my fights meticulously and will pregame them all - 1st level characters don't fight anything that isn't a planned and set fight.