When one applies for an academic position (especially for a permanent one) or for a significant funding, (s)he is often asked to show his/her professional maturity in research in the motivation letter/research proposal (or sometimes one is asked to indicate how (s)he would reach this maturity).
The questions is: what are the signs of professional maturity in research that might be mentioned?
My background is theoretical mathematics but the question has little to do with a particular field as usually the positions and funding in question are for researchers from a broad range of scientific areas.
Independent research done. I.e., not as part of a guided thesis, not as a junior member in a research group or postdoc. Number of publications as sole author, or at least publications with a variety of coauthors (not just a flurry of papers with the advisor).
More broadly, all research is relevant, the more the merrier; but I'd stress the above points when evaluating proposals (or a colleague for promotion).
I'd say just go for it. Show all you have. If they reject your proposal, you can certainly use it to build the next one. If you don't apply, I'll guarantee you won't get it.