Will the DLC transfer over if I restart my game?

The servers providing the additional content were shut down by Nintendo quite a while ago (specific date needed), so you won't keep the guests in Stornway and the extra Quests. So using the normal way you won't be able to obtain the content, although it may be possible by using an emulator and some cheats which manipulate the ram, but that is not the proper way.

There is still a way to access the DLC content, including the extra quests, legacy characters that stay at the Stornway Inn, and daily DQVC specials.

Before the Nintendo Wi-Fi Connection service (WFC) was deactivated in May 2014, a few people/groups began to capture the DQVC (and other) traffic, and have replicated those servers.

By redirecting your DQ9 wireless connection through their DNS servers, you'll be able to access most of the same features that were available while WFC was active.

1. You must have access to a Wi-Fi connection with either:
   • Security disabled, or
   • Security enabled but using only WEP: See below for notes and some suggestions
2. Launch (or restart) DQ9, and you should get to a menu with "Continue your adventure", "Delete adventure log", and "Configure Nintendo Wi-Fi Connection settings".
   • If you do not see this menu, it often means that your last save was a Quicksave instead of a full save: load the Quicksave, travel to a save point like a church, do a full save with the Priest, and then restart DQ9.
3. Within the "Configure Nintendo Wi-Fi..." menu option, create or update one of the three available Connection slots to use the Wi-Fi connection from step 1.
   • You will need to enter its SSID
   • If the Wi-Fi connection was setup using WEP, enter the WEP key
   • Scroll down to find "Auto-obtain DNS" and select No
   • Under "Primary DNS", enter either wiimmfi's DNS 164.132.44.106 or altwfc's DNS 172.104.88.237
   • Test and save the connection
4. Go to the Stornway Inn and speak with Sellma to access the DQVC content. In addition to downloading the daily special (which does change daily, by the way), the first time this is accessed, it will also:
   • download all remaining DLC quests
   • unlock legacy characters that stay in the Inn (use the elevator in the top-left to access visit them)

You will need to setup the Wi-Fi connection within the game itself. If you play DQ9 on a newer system, such as the 3DS, you should not modify the 3DS' internet settings at all. It's important to note that DQ9 was released before the better protocols, like WPA/WPA2, were around, so the game itself is incompatible with these newer protocols. Even if your 3DS and newer systems are already connecting to WPA- enabled routers, you can't use them for your DS game.

I found that most modern laptops (Windows, Mac, Linux) and even some desktops with Wi-Fi built in (or available with a wireless dongle/card) are able to create and share their own Wi-Fi connection when they are plugged into an Ethernet cable. These connections can be created with no security, or using only WEP security, which you can connect your DS/DSi/DS Lite/3DS/3DS Max to while you play. (FYI: You can use this for all sorts of other DS games besides just DQ9.)

When I set up my laptop to share its WEP-enabled Wi-Fi, I disabled broadcasting the SSID. Since DQ9 only requires about a 30-second internet connection to download the DQVC store content, I usually enable and disable the Wi-Fi connection on the laptop for that brief window.

(Thanks @T.J.L. for the edit suggestion!)