Moving Navigation Above Twenty Eleven Main Image

once you have a child theme of twenty eleven setup and working, this should be possible by editing header.php in the child theme, and moving the full <nav id="access" role="navigation"> section to above <hgroup>.

the rest is fine tuning of the styles, if neccessary.

without causing any issue with my site

impossible to tell, as there is no link to your site in your post here 🙁

the importance of working from a child theme is to have an unedtited default theme as a fallback in case of theme problems; also to avoid loosing all customisations when uprading the wordpress version.

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you should be fine following my initial suggestion:

in header.php, the section to move is starting with (and inclusive):
<nav id="access" role="navigation">
up to (also inclusive):
</nav><!-- #access -->

move that to directly after this line:
<header id="branding" role="banner">

make backup copies before editing.