email address with @icloud.com domain

Your Apple ID should have by default an iCloud email associated with it. You can change it to use that instead of your gmail email address, but in all honesty, it is not recommended to only have an iCloud email as the Apple ID, as in the event something happens and you lose access to the Apple ID you also by extension lose access to the iCloud email and as such would be very difficult to recover access.

Its recommended you keep a 3rd party email address as part of your Apple ID, it does not need to be the main email, but can be the rescue email so you can recover the account in case of something going terribly wrong.

See here: About your Apple ID email addresses - Rescue address - Apple Support

Also note that once changed to the associated iCloud email address, it can never be changed to anything else, ever again.

From the link provided by Fox:

Enter the email address that you want to use. If you choose a me.com, mac.com, or iCloud.com address, you won't be able to change your Apple ID email address again.

See instructions in Change your Apple ID - Apple Support

Based on what I have read, I suggest you leave your Apple ID email address as a 3rd party email address because you have more flexibility if you need to change the email address. For example, if the Apple ID got compromised, you can change it to another address. I also have read of many people who were locked out of their accounts when they forgot their password. Since the recovery email address is the @iCloud email address, if you forget your password, you also can't access your email to get emails from Apple to recover your account. You can set a rescue email address, but for some people, this hasn't worked.