In my view, I'd suggest keeping your domaining business separate. That doesn't necessarily mean you need to create another LLC; putting them in your personal / dba name may be sufficient. Point is keep the web design business separate from the domaining part.
In the web design business, disputes are likely to focus on web design not being what the client expected, disagreement over the price, and issues relating to updates.
If you are also providing webhosting and/or ecommerce solutions, the common disputes involve lost data, website downtime, design flaws / programming errors, and client's lost business due to any of those reasons, and/or others that are totally outside of your control - ie. client has FTP access and uploads an update on their own that causes their website to malfunction ... it's their fault, but often the client, often out of sheer ignorance, will blame the webhost provider for any problem that occurs.
A well drafted contract that clearly specifies what you provide and what are you aren't responsible for is critical - you can likely find free / inexpensive boilerplate web design / web hosting and related contracts to use. I'd suggest seeking those out so you have something to use right away, as well as getting an idea what such contracts often include, before contacting an attorney to fine-tune them to your specific business. In short, a set of well drafted contracts will go a long way to reducing your liability exposure.
Ron