You'll probably feel a bit odd - until you test, you won't know which "oddness feeling" is actually hypoglycaemia. Once you know and can recognise hypo feelings, you can treat with jelly babies etc before testing. Personally, I always ensure I have some sweets in my pocket, or bag if wearing clothes without pockets, or bumbag hanging from bedstead at night. There's no point risking going down stairs / get out of bed etc, when you can treat hypo without moving.
You should inform DVLA, who will post you requirements for drivers treated with insulin - that sheet is not available online, as far as I can find. Basically, test before setting off, don't set off if less than 5mmol/l, stop & test every 2 hours on longer journeys, always carry sugar and longer acting starchy food in front of car (so you don't have to get out of car to get things from boot, for example), if hypo, take keys out of ignition, move out of driving seat and wait until recovered - DVLA says 45 mins from detecting hypo.