can my dog become pregnant at 10 months

Yes, your dog can become pregnant at 10 months and, yes, it's possible the male can impregnate her.

I would do some research on the subject.

Would she have health problems if she got pregnant at 10 months - is that your question?

Again, use google and do some research.

Yes, she can become pregnant. The situation you are describing is how a lot of kennel 'accidents' happen.

Are you planning on breeding either of them? If not, then you might think about having him neutered and her spayed after her heat is over.

Can you keep them apart for the month that she will be in heat?

The answer is yes, she can. However your young male may not know how to go about it.
But don't count on that. There is always the chance that she get out by mistake or some lonely male enters your yard without your knowledge.
Believe or not I've seen a male trying to get to one my females years ago through the fence, if you can picture that.
Should she get pregnant? Absolutely not.
She is a puppy herself, still growing, in mind and body.
Not only could pregnancy put her at risk, trying to deliver would put her at risk, not to mention the risk of delivering dead or improperly formed pups, and you may have to raise them yourself.
I would suggest keeping them totally separated and seriously consider having them spayed and neutered.
Altered pets make for happier healthier house mates.