You need two things:
- English Class
- Switches and Variables Tutorial (any will do)
The second one explains you all you need, however here it is in short: Set up a variable called Kill_Dog_Amount (or whatever you prefer), and raise it by 1 every time you kill a dog (if they're defeated together, all you need is a switch really). The event you're supposed to get another quest will now get the mentioned conditional branch, asking for the previously introduced variable Kill_Dog_Amount, and set to react if it is at least at 2.