"Twenty years from now you will be more disappointed by the things that you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover." -Mark Twain
Go for it! If your training for a marathon and doing back packing trips like that, you'll be fine. When starting out mountaineering it was difficult for me considering my exercise educed asthma and such. But running has helped push me a long ways. But keep in mind that June can sometimes have some pretty nasty weather. Last year we called it June-uary. If you went for it last year you would have had crummy weather on your attempt. Make sure your crampons fit your boots. A partner of mine learned the hard way.
(literally, his hands were bloody by the time he got them on)
Now had you not been going with a guide service I would have thrown in more cation. But they know what they are doing. But don't expect it to be drama free. I've seen rocks fall a lot on that mountain.