I would say its fine to filter and bottle but wouldnt drink it for at least as month as that would surely put a lot of stress on the wine and that usually changes your profile temporarily, especially bottling it.
I usually filter 2-3 carboys then bottle the next day. It's mostly a time thing. The answer to your question is yes, you can filter and bottle the same day. The bottler that I have actually has a filter accessory so i can filter and bottle at the same time! As Wade said let your wine rest a month before drinking. Thats if it didn't need any more aging.