You don't say where you are located but if you are still having nights that drop below freezing a tree with peaches already on it was unlikely to have been grown in your area and was brought in from a warmer location. Acclimation, including the dropping of any nascent fruit, is to be expected.

It is also suggested not to let newly planted fruit trees bear any fruit for at least their first season and depending on their age, even the first couple of years in the ground. This is to allow sufficient time for them to focus their energy on developing a good healthy root system.

No, it will not produce another crop this year. Fruit comes from the fertilized (pollinated) flowers and since all flowering is done for the year, no more fruit. And as previously stated, you don't want it to produce any fruit now anyway. Not until the tree is properly established.

Thanks. We're in zone 5a. Tree was purchased in 5b. At 6'-7' tall, how many years should I remove the fruit?

6-7' is still a baby. I'd remove next year's fruit as well. Proper establishment and a healthy, well-developed root system is far more important than a few young fruit.

When do you determine that you can let it bear fruit if you don't know the age? Height or trunk diameter? Or at this height is it just letting it settle in for one year to get established? I'm going to be picking up a reliance this weekend as well and it should be the same size or slightly larger.

It is more a matter of time planted in the ground than it is the actual age of the tree. Most fruit trees sold at nurseries and garden centers (and virtually anything available from mail order sources) are 1-2 years old. So they are very immature. The rule of thumb for fruiting is 2-4 years after planting, depending on the tree