I'm curious, how many visits and pages do you get on a daily basis from the search engines. Currently I have a website that is about a week old and for some reason MSNBot is crawling it daily (about 400 pages daily so far)
Not really that important how many crawls you get - the main question is are the pages being indexed, and if so, are they ranking?
If your site's only a week old, give it some time - it can take time for information to filter into the search engine's indexes from the crawlers. Also spend some time getting links to your website from other websites - if you want your website indexed faster and ranked higher, this should be your main priority.
The SEs crawl your site and then start making calculations and 'thinking' about your site before it gets put in the index so sometimes there can be a delay of a few days.