This is interesting. I believe all the apps on Google Play a pre-screened for malware, so it should be ok if the source of apps are credible. On the other hand, I'm wondering if browsing can induce malware.
Not a security expert, but I think the short answer is yes, but the likelihood is very small.
I think it is sort of like the issue with Macs, where it wasn't that Macs were impervious to viruses, but rather it was that 99 percent of viruses were targeting Windows Machines and Macs made up only a tiny fraction of OS's in the computing ecosystem. Of course that has changed now, and we hear about viruses on Macs pretty frequently. I don't think many viruses are being written to target Android phones. I am sure they are out there, but I am not sure they are all that effective or that anti virus apps are all that effecting protecting from them.
So far as I know non-rooted Android OS doesn't have Flash and Java (somebody please correct me if that is wrong) nor do they have Windows programs installed and running, and I think those account for the vast majority of viruses. But simple browsing? ..............Hmmm, I just doubt it..........simple browsing but watching video, more likely.........If you are browsing known virus-prone sites, or if you are browsing with the belief that you can't get malware and don't exercise caution, or do not follow the good security practices you should be using already on your PC, then yes you'll get malware.