As others have said, you're not "forwarding" the subdomain, you're just setting the DNS for the subdomain to the IP address of your home server.
You have a few options:
1. Manually set the IP address of your subdomain whenever you get a new IP address for your home connection. You do this in the panel under "Domains>Manage Domains". Click on the DNS link for your domain and add a DNS entry for the subdomain you want to point to your home IP address. Oh, make sure you set the "A" record.
2. Use a service like dyndns. You can use the free service to get a yoursubdomain.dyndns.org address. There are a variety of ways of getting your router to automatically update the IP address at dyndns to match it's external IP address.
3. Do #2, but then add a "CNAME" record for a subdomain at dreamhost that "points" to your dyndns subdomain.
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