Design is so difficult to quantify.
I am in a similar position working for a sign company for the last 20 years. I sell the signs and also design them. Sadly we can't charge up front for design but try to include for it in our pricing.
Where you can go wrong is to spend say 3 hours designing something and quote for that and then have the customer change his mind about layout etc. You then in effect have to start again, but if you have given a fixed price you will then make a loss as the customer will say that you have already charged for it.
You could say to a customer that you will produce a basic website ( and show him an example or template ) for a fixed price - say £500 ( if it will take say 10 hours to design ) but that for every hours design over that you will charge £50 per hour.
Once you have a few under your belt and can show them to potential customers then you could up your prices.
It's a balance between pricing to make sure that you get the work and not selling yourself short. It's pointless trying to get £100 per hour and only doing one a year because your potential customers can't / won't pay that price.
Only my opinion though
