Hey,
I would like to trade a token with a fixed price of 1$ on Uniswap/Pancakeswap, etc.
My understanding is that I need to create a pair with some other stablecoin like USDT/USDC and put 1:1 liquidity
Is this correct?
Hi, welcome! 
I think Uniswap/Pancakeswap is an AMM DEX, it has slippage based on the liquidity.
I think you need a DEX, maybe like the Order Book Pattern in the Centralized Exchange.
What about other stablecoins on DEX, How do they get their fixed price?
I think they have the pair on many DEXes, for example, if you want 1 USDT = 1 USDC on uniswap, when someone sells some USDT and make the new exchange rate to 1.1 USDT = 1 USDC, others will use USDT to buy USDC on another DEX that its exchange rate is still 1, and then sell USDC at the uniswap. This is arbitrage on different DEXes when there is price difference.