After creating an A DNS record for WWW is it also necessary to create a AAAA record for WWW?

I'm using an A DNS record to translate WWW for IPV4 traffic. It looks like this:

DNS records

TYPE: A

HOSTNAME: www.mywebsite.example

VALUE: directs to 192.168.0.1

Do I need to add an AAAA record for WWW to support IPv6 traffic?

To answer the question in your headline:

No, it is not necessary to create an AAAA record for your website as long as most traffic runs over IPv4, but I would argue that it probably is beneficial for the deployment of IPv6 to have more sites support the protocol.

To answer the question in your post:

Yes, if you want your site to support IPv6 traffic, clients need a way to translate your domain name to an IPv6 address.