To use your Laptop as a "Router" in the sense of giving your DS the possibility to go online, your wireless Lan built in your laptop needs to be able to run in infrastructure mode, the mode in which routers and Access Points run and are able to accept wlan clients and sharing the network with them. Ad-hoc mode is not gonna do it for the DS.
So use google and see if the model of your built-in WLAN supports infrastructure mode through means of custom firmware or software forcing it to run in this mode.
If it works this far, you can just configure a WEP and Mac Address restricted WLAN access point on your laptop, so you have at least a minimum security if you run this WLAN in a more public place and put the connection details into the DS.
This should work in theory and does not require any homebrew on the DS, as far as I know there isn't even any DS homebrew like this, only others where the DS can be used as a mini screen so you can access your laptop or use the DS as a controller, but this is all homebrew that already requires your DS be in the same WLAN like your laptop so a connection between them can be made.
Note that of course while you use your laptops WLAN to provide internet to the DS, the Laptop has to get internet connection somewhere else from, connected to a LAN probably.
You can't have the WLAN running on your laptop allow connections to it and on the same time receive wlan access from somewhere else, possibly a real Router, at least not running from the same WLAN chip.
Hope this wasn't too much techno-babble, but if you want your laptop to provide internet to the DS, its gonna work like this.
Don't expect that your built-in WLAN in your Laptop is gonna be able to provide infrastructure mode, the are only a few chips that are able to, with a little work done. The Laptop is simply is not designed to be an access point, that's why WLAN access points like the Nintendo USB Connector exist.
I would refrain from buying the Nintendo USB Connector, its long time not supported by Nintendo anymore with new drivers and I only was able to use it properly while I had been running Windows XP on my laptop and having modified drivers and software to use the Nintendo Stick like a real access point. Since I have Win 7, I was never able to run it again properly, so you are better off asking for recommendations for other hardware.