I am working on non-human species data and i have used VQSR in the analysis pipeline as shown below:
If VQSR is performed, should we still consider filtering the variants on basequality and mapping quality?
In humans, we do not use dbSNP at all for VQSR training or truth datasets. This is because we are not very confident in the variant calls. As for other organisms, we cannot comment on the use of dbSNP, but it is likely you should not use a high prior. Have a look at this article for recommendations on running VQSR: http://www.broadinstitute.org/gatk/guide/article?id=1259
If you can find a better dataset of variants for your organism, you should use that.
Another option you can try is to make your own truth dataset by doing hard filtering. Please read about how to hard filter you data here: http://gatkforums.broadinstitute.org/discussion/2806/howto-apply-hard-filters-to-a-call-set
Once you have this hard filtered dataset, you can use that as truth set in VQSR.
Please note it is difficult to get a high quality variant set for non-human organisms, and some experimentation will be necessary.