Basically, yes. Keep the primary covered with cheesecloth or muslin to keep out fruitflies, etc.
A month is not nearly long enough for your wine to be finished, though. It will keep throwing sediment, and you should rack every 30-60 days off of the lees. When it's done fermenting, and done throwing sediment, that's when you can stabilize, sweeten (if necessary) and bottle. I have 5 gallons of blackberry that I started on May 4 and I'm now oaking and aging. The key is not to rush it. I just opened one bottle of dandelion from this year, and it's good but really way to early. It should age 6 months to a year (after bottling) for best flavor.
A dry wine will finish in the ballpark of .990-.998 usually.
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