The chlorine dioxide treatment that Aqua Mira provides is about the most effective treatment on the market, and probably the best thing you could use to ensure your daughter's safety in any water situation you are likely to encounter. Unlike the proponderance of water filters, Aqua Mira will take out viruses, which while rare, probably represent the greatest health threat to a toddler.
Chlorine dioxide is in widespread use in municipal water systems as a primary disinfectant, but unlike municipal water, Aqua Mira does not include any free chlorine residual like is added to municipal water (after treatment) to ensure safety between the treatment facility and the point of final consumption (i.e. while in the distribution system).
Bottom line is that chlorine dioxide treatments should be just as safe as your tap water at home, and safer than just about any other treatment option in the field.
UV light treatment like the SteriPEN uses is another good choice, but depends upon having fairly clear water for reliable treatment. I can not always reliably find clear water everywhere that I go, so I think less of this option.
If your water source includes large particles, you should make some effort to prefilter before using any treatment method. I find that running it through a bandana is usually sufficient to knock out the objectionable particles.