It's Not Possible
You have asked for a Science-Based answer, and it's just not going to happen. Despite what Indiana Jones says, it's impossible to build a nuke-proof fridge. Even if the fridge itself is basically OK, the concussive force it went under would jar it severely (and rattle anyone inside of it to death) - or the heat of the blast would cook you inside of it.
So to answer your question about what I would make it out of, since I'm selling snake oil anyway I would build it with the CHEAPEST things I could, put a basic lead plating around it all so people thought it was built in a sturdy fashion, then make profit. And shortly after selling a few I'd close up shop and drop the alias I was using.
If I were to try to answer this more to the spirit of your question than how it was asked, to survive the nuke you would want to build the fridge out of lead (obviously). Your trouble would come where you would want your fridge to have enough air to breathe for awhile (you know the nuke is coming, but not exactly when, so you would hide in there for a bit). At that point you can either make holes in your fridge - drastically reducing its efficacy as a food chiller and as a life saving device - or install some kind of oxygen tank and air scrubber. Those however are going to take up a lot of space.
Some other downsides:
The air tank may explode due to the concussive force of the blast. And when your house is on fire, opening a door and releasing a lot of oxygen into the room will result in you being lit on fire. Of course, not opening the door will ALSO result in your death because that fridge will heat up as the house burns. If your house collapses though, it's a bit of a moot point as you'll be trapped in your fridge and won't have to worry about picking one or there other.
Because the comments pointed out the OP updated the question with a specific distance a nuclear yield, let's make sure it's still impossible.
According to NUKEMAP a 1.2 Megaton nuke has the following effects at 2km:
Outside of Fireball Radius (1.04km)
Well, that's good!
Inside or Radiation Radius (2.56km)
Less good. 500rem (5 Sv) of radiation - that's lethal! We need to get that down to about 200rem (2 Sv; the "largest dose that does not cause illness severe enough to require medical care in over 90% of people" per previous link).
The best possible shielding wouldn't be Lead, it would actually be Tungsten. To be safe, we'll use two halving-factors, which would actually reduce radiation to ~125rem (1.25 Sv; a hair over the "Smallest dose causing loss of hair after 2 weeks in at least 10% of people").
Link: Half-Value Layers
If we used Lead, we would need to line the fridge with: 0.98" (24.9 mm; let's call it 1" or 25.4 mm to be safe).
If we used Tungsten, we would need to line the fridge with: 0.62" (15.8 mm; let's call it 0.7" or 17.8 mm to be safe).
Well, that's possible to accommodate - you're still alive!
Inside 20PSI (138 kPa) Air Blast Radius (3km)
Per NUKEMAP, at 20PSI (138 kPa) heavy concrete buildings are severely damaged or demolished. Unless you are living underground or in a very fortunate large concrete building, per FEMA, you are dead. You cannot expect the fridge to withstand this blast.
Inside 5PSI (34.5 kPa) Air Blast Radius (7.4km)
Per NUKEMAP, at 5PSI (34.5 kPa) residential buildings can be expected to collapse. If you are in your fridge and cannot escape due to the roof having collapsed in front of the door, you will be trapped and die.
Inside the Thermal Radiation Radius (13.6km)
Per NUKEMAP, within this radius 3rd degree burns can be expected. At this point your house has collapsed on you and spontaneously combusted. If you were lucky enough to survive the pressure (doubtful), you are now roasting alive in your Tungsten-lined tomb.
There is no such thing as being "safe" 2km from any instrument of mass thermonuclear war, least of all in a REFRIGERATOR.