It's a great trip, and one I'd definitely recommend. Given some sensible planning and a bit of decent weather there's no reason why you shouldn't do it.
Get some charts and spend some time working out your route, and paticularly where not to go. The Goodwin Sands are one obvious area to watch out for, but as with most hazards around this part of the coast they are well marked.
Ramsgate or Dover would be the obvious places to stop, with good marinas and all tide access. If you choose Dover then you'll need to coordinate with the port control via VHF to get permission to enter - it's a bit intimidating but not a problem if you're reasonably confident.
If you don't stop at Dover be aware that there can be very unpredictable sea conditions outside the harbour as the waves reflect off the harbour wall.
Once you get past Dover you are fairly committed until Brighton, so do get a decent forecast before you set off. There are bolt holes on the way, but they're not ideal.