Replacing ceiling and insulation

[Toddgeraint]

Hello,
I'm hoping someone can give me some advice on the following.

I recently bought a 1920s house and am about to convert one of the bedrooms into a studio. The ceiling in the room was bowing and clearly needed to be replaced. I guessed that it was a false ceiling and pulled the plasterboard down, revealing the original ceiling beneath. This is (I think I'm spelling it correctly) "lath and plaster", and also needs to be replaced - cracks everywhere and bowing. I've had quotes on the work and basically if I can remove the ceiling and take away the rubble myself I'll save £300+.

So I went up to the attic tonight and pulled back the insulation (new, laid down in 2005) to reveal older insulation between the joists which is in small bits. I wore a mask (one of those paper-type ones that cover your nose and mouth) and goggles, and started bagging the old insulation in preparation to knock the ceiling through. Now I gather that fiberglass isn't good for you and there was dust everywhere. Do I need better protection (respirator?) and special clothes or can I just carry on? Or shall I just knock the ceiling through, old insulation and all and just keep the newer insulation up there? The newer insulation is 250mm.

I'm really not experienced with stuff like this, so any advice would be greatly appreciated!!
Cheers