For one mile, about 10 minutes of exercise at the most, do nothing.
Test your BG before hand, if <6.0 have a small snack, a biscuit or something similar.
Test BG afterwards, have another small snack if needed.
I completely understand where you are coming from, massive diagnosis out of nowhere, adn thinking how do you keep exercising. I had the same issue, with a planned 40 mile race < 2 months after diagnosis. Think short term first and then longer term, break it down into manageble chunks, get one working right adn then go onto the next.
Soem useful advice from Scott_C above. My strategy, i'm more of an endurance athlete is like this.
Anaerobic exercise - weights, yoga, swimming - I do not adjust insulin at all. I generally stay stable/slight rise for these due to glycogen release from the liver. You'll need to try it yourself, test either side of activity.
Aerobic - running, cycling, rowing, walking/hiking - tend to be BG reducing, as Scott says above. Strategies are therefore reduce insulin, increase carbs or a mixture of both. You don't say what your basal insulin is, but depending on the duration of your activity you may also need to think about reducing that as well, when I was on basal/bolus, I'd reduce my morning basal to 0.5 units before a long event, and reduce the evening dose by half to account for the increased insulin senstivity during and then after the event.
Bolus insulin - depends on timing of insulin vs exercise, if within 4 hours I definitely had to reduce dosage to avoid major hypos as I am very insulin sensitive. These days i'm on a pump and I reduce basal to 20% of normal 4 hours ahead of aerobic exercise.
You are doing the right thing wanting to maintain or start exercising as it will improve control overall and increase insulin sensitivity. What it will mean though, is that until you really understand how your body reacts, you need to 1) carry those emergency carbs and 2) test, test, test, I'd start with every half hour during exercise adn then go out from there as you gain experience, I now work on hourly on the bike, every 5km for runs over 8km. I also know through extensive trial and error that I need about 25g carbs per hour on the bike.
This is all though trial and error over the last 5 years. When you are bit more established - if you are a long term athlete, I'd look into the pump criteria, as insulin pumps can help in managing T1 with exercise.