tank size upgrade

I would put the same fish load (either the same fish or same quantity of fish) you had in it previously, and also make sure the filter you are transferring can handle the larger load of a 30 gallon. If you do that it should be fine. I'd personally give it a few days before adding a larger fish load.
 
transfering the bacteria impregnated filter and gravel and water will *help* however some will certainly die in the exchange. Plus as Dahlia said it would only have the capacity to look after the fish you had in your 10 gallon.

Personally I would fishless cycle the new tank to be safe.
 
I think you should be fine as long as you keep the top layer of your substrate damp, dechlorinate the new water*, and use most/all of the decorations and filter **from the other tank.

*There is no need to transfer your dirty water from the 10g tank to the new one because extremely little bacteria is free floating in the water.

**I would get a new filter for the tank like an Aqua Clear 300 and turn the flow down and use it contemporaneously(where they heck did I pull that one from?;)) with the other established filter for about a month or so so that the bacteria has time to grow on the new filter. Then, after that time, you can take out the old filter and maximize the flow.
 
I agree with NJ, especially about the top layer of substrate. Do you have a wide mouthed siphon? Use it to get the top 1/4" of gravel into your siphon bucket. Pour off the water (but leave an inch or two in to keep the bacteria alive), then transfer the rest of the contents to the new tank. When that is done, carefully spread the top layer gravel evenly over the top of the replaced gravel.
 
I recently did the same change from a 12g to a 26g with no problems whatsoever, but I did have a light bioload. As pointed out, not necessary to transfer all the water, if your replacement water is OK with respect to pH, temp, etc. Just continue to monitor your parameters daily as you could get a small ammonia spike from all the mucking around, but the bacteria could probably handle this. Would be conservative about any rapid increase in the bioload ( i.e., new fish ) until you are certain no problems with the switch. Although fishless cycling is a wonderful, humane idea, this is one of the situations when it is really not necessary and gives no advantage.
 
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