What part(s) are you having issues with?
For your project.. doesnt seem to need an RPi.. does it? (why?)
The 'dog feeder' project has been done a million times over...
I'd suggest you search for some of these.. and get a idea in your head on how you want YOURS to behave/work.
First things..
work out the mechanical aspects..
Hopper? dispener? auger?
You still have the same question as above... how do you get your pet to get CLOSE ENOUGH to the RFID reader? the distance for it to work is very small..
The rest is very basic 101 tutorials..
RFID
stepper or servo
code
etc..etc..