Of course you can do it this way, just make sure to have the new tires on the rear axle. Even with front-axle driven cars you never should use the new tires at the front, because having old tires on the rear axle leads to heavy understeering (tail drifting) while cornering on wet roads...

I think it is okay to do it this way, and as already mentioned make sure to have the new tires on the rear axle.

If I was you, I would wait until I had the enough resources to get the four tires. I would install the four tires at the same time, so the next time that you would need to change them you would change the four of them at the same time, knowing that all of them are at the same wear level.