I very much love salah in its prime time and I do it if all the time. I have classes that take place during 1:30pm whilst salah dhuhr is at 1:30pm and the class is a 30 minute walk away so I have no way of praying on time and will have to miss my salah.

I don't want to just pray namaz whenever i get the time, I want to pray it as soon as the time arrives. But my situation won't allow me.

Do I still get the rewards of someone who prays Awal Waqt (on time at the first minutes) if I pray namaz as soon as I get home?

As long as you show concern for your Salah, and you feel bad for having to delay it, and you could not find a practical way to offer it right on time, then you would not be considered as negligent with your Salat, and hopefully you will be granted the full reward. But make sure that your Salat never becomes Qadha’, as that is a major sin. As long as it doesn’t become Qadha’ then you are ok.