Yes you can do this, but you have register all four dns servers for your domain name. There are no duplicate penalties involved if both the site at webhost 1 and 2 have the same domain name. Search engines see them as one site on multiple IP addresses. If host 1 goes down, visitors may still have load problems because in 50% of the case the DNS server will return the IP address at webhost 1, even if that server is unavailable.
An alternative is to use a third party DNS provider. You normally point the A record of the domain to the server at webhost 1. If that server goes down, you point the A record to webhost 2. If you use a small TTL (time to live) on the A record, the switch will be quite fast and visitors will only face downtime during a small period.