You're asking too much. Even if you've asked for a simple light tracking robot (the photovore) I would have asked about the "shape" because it matters. This is not going to be an single algorithm but a bunch of specific algorithms with an expert system overseeing everything. Here are some pointers:
Your robot runs on wheels? => You'll have an algorithm for controlling speed and direction.
Your robot has legs? => You'll have an algorithm for walking (something called an GAIT). This stuff is difficult.
Your robot has an arm so it can put the fire out? => You'll need to do Inverse Kinematics, lots of fun, lots of math (hope I'll do that some day).
Your robot needs to identify the "doll"? => Unless you expect the doll to be marked with some kind of special marker you'll need to do Computer Vision. That's very difficult. In my opinion the technology to identify ANY doll in ANY environment doesn't exist yet! Be the first to create this algorithm and you'll become super-rich and get a Nobel price!
Add everyting together and you've got a challenge. When does it need to be done?