I use an ethernet connected Samsung laser printer that takes only about 30 seconds to warm up from a cold start power-up, and then be ready to print.
Possible problem solutions:
1. The fact that the device is multi-function: both a printer and a scanner, which could be slowing down the process.
Use separate printer and scanner devices?
2. The router being used. Upgrading to a router with gigabit ports could provide improvement, or else a firmware update for the router.
3. The official Brother MFC-7440N driver is dated 11/24/2009:
http://support.brother.com/g/b/downloadlist.aspx?c=us&lang=en&prod=mfc7440n_all&os=93
It may require replacing that device with something more recently produced to overcome the 5 minute delay problem.
4. The ethernet cabling could also be something to double-check.