Nathan, in short yes and no!
Your match rod etc will be fine as long as you upgrade your line according to where you are going to fish.
There is no reason why you cant catch carp on match tackle but you must realise that the average size of your fish SHOULD be much bigger so you need to up the breaking strain of your line.
I've caught plenty of carp on the float.
pick a relatively easy water and ask people about tactics and baits.
To move into ledgering for carp would suggest that you are going for bigger fish.
Your match rod will handle just about any fish you could hook but thats not the problem. Your terminal tackle will weigh a lot more and if you try to cast that with a match rod you may end up snapping it. Just as I did with a light rod two weeks ago. I should have known better but it was all I had with me.
Read up about tackle and tactics, there are loads of article on this site, just search for them.
Carp tackle is not cheap so you should be sure that you want to pursue carp fishing before you pay out for gear that you may not use.