Even if your online store is mainly focused on dog products and even maybe has the word 'dog' in the domain main, it would be wise to have a 'Other pets' section. This could be the minority of the site, but remember... people who own a dog, may also have hamsters, gerbils, fish etc etc It may be easy for them to utilise the 'joint' P&P costs and order a few items. This is called cross-selling.
The more products you sell, the higher the sale to visitor conversion will be on your site, as you are more likely to have something that someone would want.
Also, definately do your research in all the major stores, like it sounds you have done, or are doing. See what types of items they are not stocking and target them. With supermarkets, if they are not selling something, it is for a reason. There dedicated shelving space may be better something else, but that creates a niche for other people. Find those niches / products and target them.
Small and light items are best for online as you have to ensure that it is worth while people paying the P&P. Offer incentives, and maybe offer a monthly prize draw for ALL your monthly newsletter readers, and then add a newsletter sign up to your site.
The utmost important factor is SEO. If you don't rank well in the likes of Google, then you will have no online business. Forget PPC campaigns such as adwords if your products are low cost. Target organic listings, and deep link to all your inner pages and products.
Good luck!
Andy