Just expect the slate to be heavier than you expect it to be (does that make sense?). If you've never carried slate before, it can catch you off guard, especially if it is a 9'. Smaller tables are not that bad. Also make sure you're carrying correctly. It's very easy to get your back twisted up if you're not carrying properly with the other person.
I would also correct you by saying the slate SHOULD not break. The reason I recommend having a pro do it though is they have carried slate before and know how to do it without hurting their backs. And on the off chance something happens and a piece of slate DOES get broken, you're not out the money for a new piece/set.
I've just seen way too many tables that people try to move on their own and it turns out bad. Dynamo bar box for example that I sold an hour and a half on eBay. The buyer insisted against my recommendations on picking up the table themselves. They showed up with a trailer and 4 people put it on there. 2 days later, they called me wanting to know what I was going to do about their broken slate. Shit happens, as they say. They were out almost $600 more to pay me to drive an hour and a half the wrong way to get a new piece of slate, deliver it to them and recover it. I offered to deliver it initially for much less than that.
I'm not saying you can't do it, but sometimes for the difference, it's just worth it to let the pros handle it.