Your best bet would be to purchase a corded handvac with revolving brushroll like the Dirt Devil Ultra Handvac M08230X. It is a proven design, that has been around since the 80's in the plastic form. Royal made it in the metal form even older than the plastic design. With the corded models, you can clean the stairs or furniture with no time limit. It uses a shake-out bag or you can use a paper bag. Dirt Devil also has a few other models that use pleated filter. With these, you will have to make sure that you clean the filter very well after each use. Check out the Dirt Devil Classic Handvac M0100 or the Dirt Devil Power Reach M08245X. With the Eureka mentioned earlier, you will also have a filter that you muct keep clean after each use. The Dyson's filter will do well, but you will have a very short time to clean before recharging, plus the cost of the Dyson is high. You did not mention what brand and model of upright vacuum you have, but you can purchase a mini turbo attachment. This attachment will use a revolving brush, that will do well at cleaning up pet hair. Here is a link that might be useful: Dirt Devil Ultra Handvac

My suggestion to you is to look at corded handvacs. They will have quite a bit of power. Cordless handvacs will give you a short amount of time before running down. After a few years, the battery will not charge up like it did when you first purchased it. Find a good corded handvac that has a revolving brush. This will make cleaning carpeted stairs easy. Dirt Devil has the Ultra Hand Vac, Power Reach, Purpose for Pets hand vac or the Classic. If you want to, you could even purchase an extension cord, for vacuum cleaners, and vacuum further/longer without moving the plug. If you want to go with a cordless hand vac, look at one with a revolving brush like the ones from Euro Pro. They clean quite well and hold a charge a bit longer than the dyson. They are alot cheaper than the dyson also.

This may be overkill but I have it and use it as a mini shop vac, it can pick up sawdust etc and the wand is a great feature. Black & Decker FHV1200 Here is a link that might be useful: Black & Decker FHV1200

I have the Dyson V6 Motorhead and love it! The 5-7 minutes is only when you set the power on high. Otherwise, it's 20-22 minutes of power between full charges. 2/3 of my house is Saltillo floors. The rest is medium high carpet. I never had to use the high setting even on carpet. It cleans very well and recharges quite quickly. I like the fact that it's a stick which makes it easy to vacuum under low clearance areas. In other words, the dirt/dust bin is not a lower end as with the other brand models. I also have a Dyson upright but haven't had the need to use it since I got the V6. I did a lot of online research and read many reviews before settled for the V6. For someone in a wheelchair like me, the Dyson V6 is most convenient. No cord or vacuum hose to run over or wrap around the wheels. I can move in my wheelchair easily during vacuuming with the V6. I accidentally found out about this model while watching a Korean show. I didn't know that Dyson came out with this cordless model for a few years now. Wish I knew it sooner.