personally, thats too fast for my taste
i usually go quite fast, but i will always have 5 light frigates plus my cap, and by the end of 3 planets or so, i will have 5 Long range frigates, and maybe 5 more light frigates... depending on the type of planets....
i like to play medium to large maps, so i expand to a point where i have a fairly good economy between all my planets, then hunker down and wait till i have the resources to build up my fleet, do research and defend my empire effectively. usually (and on the map i have in my mind) i expand aggressively and quickly enough to secure my empire (usually i expand till i reach a good choke point or 2 from which to defend my empire), then calm down a bit... then, when im forced to or have sufficient means to defend myself and have a fleet big enough to advance, i move on.
there is another map i have in mind where there is only one planet that allows you to get to the star, and then to another system with lots of resources. in that case, i expand or even jump ahead till i reach that planet, fortify it, then work my way back so i cant be seperated from the bulk of my planets.
i have to say though, the rate of expansion depends on the size and type of map... if there are alot of neutral resource extractors (i.e. in plasma clouds etc) then you can probably hold on on colonising too fast, on the other hand, if its a smaller map, you might want to focus on finding a good choke point, fortifying it, then taking the rest of the planets at leisure... it really depends on the map, the race you are playing and your playing style...
i remember the first game i played, i went to another planet with a a milita, thoguht it was the bad guy, and didnt colonise it until the end of the game... dont know how i screwed that up, but anyway, keep playing, you will figure it out.... good luck