An oak has self seeded in our garden. Has got to about a metre tall and seems happy. We don't have anywhere near enough space for an oak but seems a shame to kill it. Can we move it to a pot to keep it dwarf?
Oak trees are well suited to bonsai, but that is not your biggest problem here.
You have two main problems: getting that thing out of the ground with its root system in tact and secondly getting it to survive once it comes out of the ground.
Getting the tree out of the ground, even though it appears small isn't an easy task. I can't find a reliable source right now, but you will need to dig a circle with a diameter the same size as the height of the tree and you will likely need to dig at least the same length deep. Young trees usually have one long main root and if you damage that your chances of the tree surviving are slim.
Professional bonsai growers who grow their own trees in the ground usually wait for a rainy day to dig out the plant so the ground is soft and the clinging soil doesn't pull so hard at the roots.
If you are not purchasing nursery stock to "bonsai" then you need to acclimatize the plant to living outside of the ground for 1 - 2 years before putting it in a small pot where it will be restricted in terms of moisture and the size of its root system. So initially you will need to put it in quite a large pot with plenty of soil.
Make sure you keep the soil well watered at least for the first 3 - 6 months. As the soil in the ground is kept moist and protected from the sun, but inside your pot it can dry out easily and the plant doesn't have the breadth and depth of a root system of trees in the ground.
Lastly I'd like to say that this is not an easy task, it actually requires practice and has a low success rate as small trees are not hardy. Our neighbours have a sweetgum (Liquidambar styraciflua) that provides us with around 30 small trees a year, but only about one a year ever survives past 6 months and that's keeping it in the ground.
I've tried this several times myself, but in the end, I can with much less effort buy a year old, acclimatized bonsai starter for $3 from my local bonsai nursery. It's not worth the sweat and strain just to see your treasure drop its leaves after 2 weeks and die. The same thing is likely to happen in the ground anyway.
Of course I also checked with a local bonsai expert to make sure that I would be able to do it "right" without hurting the 6 inch high self-started seedling. If I had been told I couldn't do it without killing it, I would have planted it at the edge of a neighbor's field - with permission, of course. So far, so good.
I'm no bonsai expert, as basically that is what you are talking about, when artificially keeping a tree small (via various pruning methods).
As far as I'm aware, nearly all tress can be used in the practice of bonsai. That's not to say, it's a good idea. Certain types, even particular variates within the same family of trees, adapt, respond much better than others, and quite simply look a lot better when subjected to the art/craft of bonsai.
I might be stating the obvious here, but simply putting such a tree (oak in your case) into a pot and watering it, doesn't mean you've finished and therefore get to sit back and enjoy your potted tree.
Yes you can put an oak tree in a pot, when doing so it would probably be best to remove it's tap root. Will it survive? That will greatly depend on how well you look after it, once its been potted up.
Here are a few things to consider:
Is it the right thing to do? Only you can answer that.
Is it (really) the right type of tree to put into a pot? Personally, I don't think it is.
It will need a lot of careful and skillful attention, especially as you train the tree to remain artificially small eg
Roots trimmed regularly.
Branches trimmed regularly.
Branches trimmed, shaped, so you end up with a perfectly scaled down version of a full size tree, or as near as you can possibly get.
Please note, I am not trying to put you off doing it, giving it a go, like they say, "Nothing ventured, nothing gained".
What I am trying to do, is make you aware of some of the work you would have ahead of you if you did decide to give it a go.
I dug an oak up 5 years ago and placed it in a gallon size container and have had much success keeping it at its original height (2 feet tall for 5 years). This spring I took it out of the one gallon container, trimmed 1/3 of the root ball off, and placed it in a larger 5 gallon container. One month later and we have leaves! Relieved that it took to the new container I will not trim any new shoots until fall. My goal is to keep it under 4 feet tall with a huge trunk. So far, so good! It has gone from a small sapling to a large trunk tree that is still 2 feet tall.