It's designed for one to five players
The Overview states what the adventure is designed to accommodate:
[...] You can run Dragon of Icespire Peak for as few as one player or as many as five players. Each player starts with a 1st-level character.
Later, in the First Session: Character Creation section, the adventure suggests an adjustment that you need to make if you are running it for only one player:
If you’re running this adventure for a single player, you can give that player a sidekick as a secondary character.
By RAW, that PC is dead, and there is nothing you can do to save them
The situation you describe, with that much damage being dealt to a level 1 PC with that little health, results in insta-death, as you know. There is no RAW way to prevent that, short of somehow being able to reduce the damage (certain classes may have certain features that can do that, reduce the damage taken by other party members, but it looks like none of your party would have had access to such abilities at level 1).
Even a half-orc's Relentless Endurance (the only thing I can of for a 1st level character, if the sorcerer happened to be a half-orc) says "... but not killed outright ...", showing that the intention is that massive damage will kill a character if that much damage has been received.
Avoiding death in the first place is the best way to prevent PC death
The best way to handle this, RAW, is to not hit them so hard at level 1. Level 1 PCs especially (level 2 as well) are very weak and I would recommend pulling your punches when they are still that level. After they reach level 3, they should be able to handle more punishment, but at level 1, they can barely stand up to goblin, let alone a CR 2 ochre jelly!
Looking at that quest, I'm guessing it was either area E5 or E7. For E5 it suggests two ochre jellies! Against level 1 PC? Are they trying to kill off the entire party!? That is well over deadly for a level 1 party. I'm not surprised someone died; if anything, I'm amazed it was just the one death.
In your situation, I would have probably just included one ochre jelly in area E5 (for E7, there is only one anyway so ignore this point if it was E7 in your case). I would have made it go for the barbarian, who can handle it, and I might also have fudged the damage so that it was lower than stated, even if only shy of an "insta-death" by a couple of HP.
You, as the DM, always have the option to use the average damage output of a monster, which in this case is 12, which would be unable to cause insta-death in nearly all cases (unless the sorcerer didn't have very good CON).
As the sorcerer was a new player, I'd have probably gone easier on them for such a tough fight, even mention how tough this thing is (in ambiguous terms, of course; not telling them it's CR, HP or damage output or anything like that), and would encourage them to think about where they want their characters to be positioned, so they can learn their party role.
The experienced players should know what their party roles are already, and hopefully have been coaching this new player in their party role (i.e. you are squishy, keep behind the barbarian, etc).
Slightly related reading on keeping squishy level 1 PCs alive:
my answer to "Keeping the world alive whilst PCs take a rest mid-adventure?"
Best Answer
Dragon of Icespire Peak goes from 1st level up to 7th level
In the "Leveling Up" section of the "Running the Adventure" chapter, it gives the following information:
There are three starting quests as shown in the "Starting Quests" section, although as it says above, completing two of will see your party to 3rd level, so you may skip one (or they can do it anyway but without earning a level from it).
Then there are six follow-up quests as shown in the "Follow-Up Quests" section, two of which are required to gain another level, so that's an additional three levels from these, taking your party up to 6th level.
Finally, killing the dragon also gives you a level. Even though this may happen at any point, it's more likely that this will be one of the last things the party will do, if not the last thing they do (when they're at 6th level). Hence this will finally see your party reach 7th level by the adventure's conclusion.
This means that Dragon of Icespire Peak will have your party still active in this adventure at 6th level (hence some places I've seen it listed as 1st-6th level, but that must be referring to the levels actually in play, rather than the level you'll reach by the end).
However, the next in the Essentials Kit series, Storm Lord’s Wrath, starts at 7th level, so I assume the intention is for the party to continue onto that adventure after completing Dragon of Icespire Peak (even though there's no narrative connection between the two, as far as I'm aware).
I personally do not have any experience running this (yet), so I can only guess how long it might take, meaning how many 4-5 hour sessions it would take, but I would guess that the party would likely reach 2nd level within the first session, 3rd level within the second session (probably half way through), and then roughly a level every two sessions after that, for a total of about 10 or so sessions. However, I will restate that this is a guess based on glancing over the adventure, not from any experience actually running it myself.