I do not think that DreamHost’s email system is capable of push email. You can do that with Gmail (by setting up using the Exchange configuration on your iOS device), and some commercial email systems, just not DH.
I use PolarisMail, which is capable of Push email with their “Enhanced” email package. Any Exchange or Open X-Change email provider will also be able to provide this feature.
On the other hand, your iPhone can be set to auto check email every 15 minutes. That’s not good enough?