I have installed bitcoin core on my laptop and noted down the wallet address and private key. I have transferred some BTC into the wallet. Is it safe to uninstall bitcoin core now?
No.
First, you haven't done what you said you did. You THINK you did that. You know you have done that when you have tested and verified what you think you did.
Next, as others have noted, there are the "Change" addresses.
Why not simply backup the "wallet.dat." Back it up to a couple of places NOT ON THE CLOUD or your computers. Be sure you are backing up the right wallet.dat too. Move the wallet.dat file from the bitcoin directory to somewhere else. Then run Core. It should recreate the wallet and read all zeros. If it does not, then you backed up something else, right?
Now that you've positively identified the file, back it up to several thumbdrives and label them.