This is advice below from google for our area. Do you know if yours are June bearers or everbearers? If you know the variety name you can look that up. The answer from below would be no either way, you will lose your fruit next year if you prune a cane that has not borne fruit yet this year.

On the fruit forum on GW, people in other parts of the country prune differently because their weather is different.

Nancy

"What Should I Do with Raspberry Plants after Harvest? This Is My First Year of Growing Them.
Growing small fruits offers lots of pleasure for the home gardener --raspberries, blueberries, and strawberries produce tasty crops without requiring much space. To take care of the raspberry bushes, learn their growth habits. June-bearing, or early-season bearing raspberries (and other cane berries such as blackberries and black raspberries) bear fruit on canes which die after fruiting. The canes for the 1997 crop, for instance, grow during the summer of 1996.

In looking at your early-season raspberries, you will note two types of canes. One type will look green and fresh, and be growing actively. These canes will produce the 1997 crop. The others will have dead leaves, remnants of bloom and fruit, and will show overall browning. Prune these canes out and discard all canes that produced fruit during summer 1996. The raspberry patch then goes over winter with only canes for the 1997 crop.

If your raspberries are "ever-bearers," producing fall crops, the situation is a bit more complex. Everbearers produce fruit in fall 1996 on canes which grow early in the 1996 season. This set of canes produces fruit during the first season -- 1996 --on the top 1/3 of the cane in late summer or fall. Cut off the fruiting top of the cane after production. The cane then will often winter over, and produce fruit for 1997 on the remaining bottom 2/3 of the 1996 cane in late June or early July of 1997. For everbearers, canes are removed from the plant after they have produced crops for two consecutive years. It's necessary to observe everbearing raspberries a bit more carefully to understand this rhythm but the plants are easy to care for once it's understood."

Here is a link that might be useful: raspberry pruning

You should leave them alone this year and they will produce next year.
Most Raspberries produce fruit on last years canes, which yours will become next year. Next year the plant will produce several new canes, for the next years crop and those that you have let age for that years fruit. It may be confusing but, left completely alone they will produce fruit year after year.

You know it's time when a cane becomes funky after fruiting. The normal cycle, when full-sized canes are being produced is grow the central stalk one year, branch and fruit on the branches the second, after which the cane declines and is cut off. The next crop of canes is then tied in to the support system.

As mentioned in a preceding post everbearing types vary the pattern by flowering two times on each cane. Sometimes this is taken advantage of by mowing the whole row off for the winter, so as not to have to bother with a support system. The down side of this approach is that you only get one crop per year, as no canes are left to fruit a second time from the previous year.

And yours plants have to be established and vigorous enough to regrow new tops every year.

There is a rather large and varied number of raspberries being grown at the Picardo Farm p-patch, if you would like to see them. Many of them must be everbearing types as fruit is present at this time.

Here is a link that might be useful: Department of Neighborhoods