Hello Eiffion
I have to agree with Steve and also give my bit of advice.
Google, like all search engines of any worth, want things you do on your site to have a real human user purpose. The problem with reciprocal linking ... "I'll link to you and you link to me" ... is that, even if the sites are realted ... does the visitor who lands on your website have any reason to follow links to another website ...
My advice is that links to other websites should always be on quality content pages, and found in the body of the page, and relevant i.e you have mentioned something on your webpage and are suggesting that if the visitor follows 'this link' they will find some further interesting stuff ... related to the reason or intent that they came to your site.
You can get some quick wins from having swapped links, but there is always the danger that Google will eventually decide the the links pointing to your site, from other web pages that have traded links with you, have little or no value and start to ignore them, you may find your site plumeting in the search results.
One thing I would advise you to do is start to search out all the listing directories both National and Local, which allow you to list your business there are lost of subject specific directories and loads with dog interests ... just search "dog" + "directory" + "add my site" or "add my Business" and other combinations and you will find lots of useful places to list your business and even get valuable links back ... but more importantly get 'Citations' (mentions of your business Name, Address and Phone number NAP) that really help to boost your SEO and local search status.
Good luck