Sooha means Red, and Saha means Rabbit. Hence, Sooha Saha means Red Rabbit, and 'Tu Hai Sooha Saha Amma ka' would translate to 'You're your mother's red rabbit.' The intention here is to say that you're cute, and very special one for your mother.
The lyrics for Highway are written by Irshad Kamil, and these are his words only.
As far as actually red rabbits are concerned, I don't think exactly red rabbits exist, but you can of course find some brown rabbits, which can be a shade of red.
For the Entire song's Translation, CLICK HERE.