You can up it to 600 then wait a week or so up it to 900. He probably hasn't checked your level because 300 would not likely make you toxic. It's really really important to have these levels checked routinely in the beginning especially. I think most people reach a therapeutic level between 900 and 1200 mg's. But everyone is a little different. Make sure you take it at the same time each day. Did he tell you morning, midday and night for taking doses? If so do that and try not to miss the doses, that will keep your levels more steady. Also make sure to drink a lot of water, and do not take NSAID's like advil as this can increase your lithium levels.

I take 900 mg a day. 600 is tooo little for me and 1200 makes me toxic. At 900 I am just below the therapeutic level. But close enough. I have started on high doses of lithium when I have been actely manic, but it's much better to go slow. But you can go faster than every five weeks. What did he initially tell you for increases time wise?