"Ponies" is such a common search term, that it's very unlikely you'll be able to optimize for that particular search term, to rank high in the general Google Search Results. "Fell Ponies" is more of a possibility, though; at least from the sound of it to me.
If you want to optimize for the term "fell ponies", you probably want to make some coding modifications to your website. Also, you want to add more content relevant to "fell ponies". The first, most basic, and easiest coding addition you can make to your site is add meta-tags; specifically a meta-description, and meta-keywords tag. These are places where you would use the term "fell ponies" and a combination of relevant terms with this term.
Also, writing more meaningful content about "fell ponies" and using that term will help. For example, if you added a page to your website that explained what is a "fell pony" and what are the differences from other types of ponies. I personally have never heard of a fell pony, but I don't know much about ponies to begin with. Regardless, a well written explanation of the differences (at least 300 words long) would benefit your website.
In general your site is kind of lacking content. Your pages with each pony you have could use some more content & descriptions. I noticed on your page for "Dalewin Maisie" you mention "Maisie was second in her class at the FPS North west area foal show and...". I assume FPS stands for "Fell Pony Show, or something similar? If it does, don't abbreviate it. Actually say "...in her class at the Fell Pony Show North west area...", because this allows you to place the keyword "fell pony" on your website again. Try getting your individual pony pages amount of words up to at least 300 words.
Finally, another simple technique that will just boost your listings overall in general; is to get more backlinks to your website (from other websites that have a Google Page Rank of 1 or higher, and preferably are related to your industry [or something in your industry i.e. ponies] or from other local businesses). I just did a quick backlink search on your website and it showed you only have 12 backlinks, mostly from forums which don't have a page rank at all. And the one website I found that has a page rank of 3, lists over 100 other websites on the page your site is listed on. The way Google's Page Rank algorithm works for determining how many points are distributed from Page A linking externally to Page B is based on dividing Page A's page rank by the number of external links it has, and giving that quotient amount of points to each page externally linked by Page A. Therefor, a website that links to your site with a page rank of 3 and has 100 external links, is about 100 times less beneficial then a website with a page rank of 3 and has only one external link. (Sorry if this sounds confusing at first.)
Also, a quick side note: I noticed when I search the term "fell ponies jedburg" (because I noticed you're located in Jedburg?), your website comes up as the 8th listing on the first page of the Google Search Results. I don't know how many competitors there are in your business in your area but, in my opinion that's a pretty good listing for your website's current situation. And could definitely be brought up to at least in the top 5 results on the first page with enough effort and the right steps. Maybe determine how close your competitors (geographically) and optimize your keywords for those areas as well.
These are only some very basic key tips that should help your site out a little bit. But the tip on writing content, and getting more backlinks; are an on-going process. The more effort put you into it correctly, the more return you'll see. And, there are a lot of other SEO
(search engine optimization) tips that you should learn that require some effort to help increase your website's listing. SEO
is an on-going process. Do a Google search on "top SEO
tips", and you'll find tons of valuable information out there. And always go back and research more, because things change; and new tips pop up or some tips become more effective over others.
Also, look into Google's Webmaster Tools: Google Webmaster Central. Get data about crawling, indexing and search traffic. Increase traffic to your site.
If you register here, you can submit your site to be cache be Google. It's a basic essential when you own a website. And it provides beneficial information straight from the people you want your website optimized for.
If you have any more questions, you can private message me for a direct conversation.