Actually, you could host just the subdomain on dreamhost without hosting the original actual domain. The problem, though, is on no-IP’s end. You would have to enter into no-IP’s system by way of their control panel thing the actual IP address of the server you’re sitting on. Then hope they don’t move your subdomain to a different server for whatever reason. Generally, it’s easier if you also own the domain name the subdomain will belong to, but it’s not required.
Also, it’s fair to point out you can set up a dreamhosters.com subdomain through the panel, and all the configuration information will be done automatically, negating the need for a service like no-ip.com, which is designed more for, say, running the website in question off your own, local machine.
Yes, I have an opinion.
Get a minimum 50% off with the “haveadreamyday” promo code, and… have a dreamy day. Original, no?