Hi Pablo,
you can find cost estimates here https://www.expat.com/forum/viewtopic.php?id=5173
USD / Guarani now is same 4.600 G per 1 USD so price quoted are more or less the same.
In general, I say yes you can live on 1,000 USD easily. However, most rental places here are let unfurnished. You can find nice places and well located at 300 USD per month, but you will need to look for a while... as normal everywhere the more you pay the quicker you find a place.
So at first you will probably spend more than 1,000 USD as you will need to buy furniture. Eg: bed, table, fridge, etc
Groceries about 150 USD maximum *actually for more than 1 person
Beer at stores:
1 lt = 1.74 USD
3/4 l= 1.30 USD
local bus 52 cents Asuncion region. Bus to other cities like Encarnacion, Ciudad del Este (farter away in the Arg/Brazil border)15 USD
fish (river fish) is the most expensive meat at 8,60 USD / kg
beef more and more expensive nowdays but nice cut for barbecue 3.90 USD / kg (vacio) and loin for steak 7 USD per kg.
as an estimate, there are open barbecue restaurants where you eat as much as you like including salads and dessert for 10 USD (drinks not included).
good luck!