Liz,
I am a little confused that you seem to have all the details of Peter's marriage but you say you have no record of it.
The entry is on the IGI at:
http://www.familysearch.orgIt lists Peter PHILP m Elizabeth ANDERSON on 19 Jun 1866 at Kirkcaldy, Fife.
If you go to the fee-paying site ScotlandsPeople (charges are reasonable) at:
http://www.scotlandspeople.gov.ukyou will be able to download a copy of the marriage certificate. With luck, it might list his mother's re-married surname.
If they did not leave Scotland until 1879, you should be able to find them in the 1871 census which is online at ScotlandsPeople.
The birth you cite is also in the IGI:
Peter PHILP, born 27 Aug 1838, bap 2 Sep 1838 at Markinch, Fife, parents James PHILP and Catherin WILSON.
Statutory registration was not introduced until 1855 in Scotland so you will not be able to get a certificate of the birth. The details in the IGI will have been taken from a church register - these are not yet available for download on SP and, in any case, they often contain no further information.
A possible marriage for James and Catherine is also on the IGI.
James PHILP m Catherine WILSON, 7 Nov 1834, Scoonie Fife
James PHILP m Catherine WILSON, 8 Nov 1834, Markinch Fife
This might not be the correct marriage but, if it is, the two entries probably represent the Banns being called in both the bride's and the groom's parishes.
As Peter was born in 1838, the earlier censuses - 1841, 1851, and 1861 - might show Peter with his mother and thus reveal her re-married name and the names of half-siblings.
These censuses are not yet available on ScotlandsPeople. However, I understand that a member of the RootsWeb Fife list does assist people with lookups of the Fife 1841 census (and, while PHILP is a very common Fife name, Peter PHILP is not so common). You might wish to look at the Fife List at:
http://lists.rootsweb.com/index/intl/SCT/SCT-FIFE.htmlGood luck,
JAP