A 2011 iMac will only go up to High Sierra 10.13.6, if you need an OS beyond that then you need to buy a new iMac. The issue is that the 2011's and earlier simply do not have the GPU hardware necessary to run Mac OS 10.14.x and beyond. Before you ask, sorry no your 2011 cannot be upgraded.
If by migrating your data to a new system, to me that means you have already gotten a newer Mac and want to migrate the data from the old Mac to the new one including applications, settings, data files etc.. This is pretty easy to do however please note machines that run Catalina and beyond must have 64 bit apps. 32 bit app will not work! This means before migrating that you need to upgrade your legacy 32 bit apps that you want migrated to their 64 bit counterparts. Some apps this is simple and you just need to update them. Others, you may have to buy upgrades or replacement apps. In order to find out what 32 bit apps you have open System Information and then click Software - Applications and the list will show what is 32bit and what is 64 bit.
Once you have have upgraded the legacy apps you want to, then backup the computer to Time Machine and then connect the Time Machine to the new Mac using a USB cable. If you have never turned on the new Mac, it will launch with Setup Assistant. SA will ask if you are migrating from another Mac, simply select YES and then follow the on screen prompts. If you have already started the new machine, the process is the same. Except launch Migration Assistant and follow the on-screen prompts. After the migration is completed (MA only) log out of your user account and you will find a new account with all your stuff.