I'm a massive gym goer and I often train about 13/14 hours a week so it is possible it just requires a bit of extra training. You can start now if you want if your comfortable
If your doing weights, then that for me doesn't tend to drop me massively whislt doing it however I drop like a brick about 2 hours afterwards.
Make sure you eat something beforehand and you must eat afterwards otherwise you will hypo. Also exercise can affect you 24 hours afterwards so you might find your a bit lower than normal. Also it might help to just test frequently when you are at the gym the first couple of times as then you will be able to find out what you personally do.
You need to take with you either Dexto tabs for if you do go low, or if your dropping a sip of lucazade is always good
If your looking for advice then a really good website is runsweet.com and that details loads of sports and ideas
The quicker you get into your normal routine the better as then you can adjust your diabetes accordingly
Good luck, feel free to message me any questions