Engineers? I need your help here with one device I want to make.?

I simply mounted a motion detector flood lamp head beside the door and aimed it down. In the base wiring there are neutral (white), power (black) and two blue wires (in my case) that were connected together and joined the infrared/heat sensor to the lamp head. Crimp connectors were used - I cut the blue wires close to the connector to replace them with wire nuts and added a wire to come inside, which I connected to 120 volt relay that mounted on a loose metal plate so it went clunk when the relay closed. I could have used a household doorbell transformer with buzzer for continuous sound. The sensor head for motion has a position for Test that ignores the night requirement and turns on the light for about 12 seconds in daylight.

In my case, the light coming on soon trained the dog it was sensed and it stopped standing at the door barking until I arrived.

You could just mount the laser lights that a garage door opener uses as a safety device across an appropriate space, and connect the output to a buzzer. It will need power, of course.

[1] USING TV REMOTE CONTROL METHOD WOULD NOT WORK BECAUSE ITS INFRA-RED CANNOT GO THROUGH ANY DOOR,WALL EVEN A PIECE OF PAPER.

[2] SECOND METHOD COULD WORK BUT YOU NEED TO KNOW HOW TO MODIFY THE EXISTED DEVICE CALLED MOTION SENSOR OUTDOOR LIGHT. IT IS VERY CHEAP ,JUST COST $10 PIECE. DISABLE ITS DAY LIGHT CUT OFF CIRCUIT FROM INSIDE SO THAT IT STILL ACTIVATE DURING DAY TIME, BECAUSE THIS DEVICE WAS DESIGNED TO ACTIVATE AT NIGHT WHILE NO MORE SUN LIGHT OUTSIDE. NEXT, CONNECT WIRE FROM ITS BULB SOCKET, LET THIS WIRES POWER ANOTHER LAMP INSIDE WHERE YOU WATCH OFTEN. BE SURE TO ADJUST THE MOTION SENSOR HEAD TO AIM NEAR THE DOOR AREA. THE WORST THING IS THIS DEVICE DETECT ANY MOTION EVEN A BLOWING TREE.

[3] I PREFER TO MOUNT AN OUTDOOR CAMERA TO WATCH THE DOG.

While the IR collar might work, the problem would be the life of the batteries since the IR leds would be on constantly, unlikely a couple of AAA batteries would last 6 hours.

Possibly a passive RFID tag on the dog's collar and RFID tag reader at the door would work. That way, there would be no false alarms as there might be with the PIR motion detector.

Your first idea will not work, because infra-red light will not go through a solid door. There is nothing wrong with the second idea. Commercial movement sensors are readily available, so you could use the output from the sensor to operate the pushbutton circuit of a wireless doorbell.