If I will move from Canada to US can I use my good credit rating from Canada when I will look for an US mortgage? I mean I will still create a history of payments in US, but if I want to buy a house right away I will have little time to do so.

Porting is for you if you get better rates in doing so. Porting is carrying over the contract to the new property. If you sell the current house with the equity and apply a new mortgage, you will be able to save on payments especially if the rates are lower now. You can then have a substantial down payment on the smaller house, have a lower rate mortgage and hopefull have some cash left.